LIST OF CITATIONS of publications by Goulnara N. ARZHANTSEVA
more then 873 citations in total, excluding self-citations.

Last update: July 2nd, 2021

Papers already published or accepted:
Summary and comments to my list of publications

[55] G.N. Arzhantseva, M. Hagen, Acylindrical hyperbolicity of cubical small-cancellation groups,
Algebraic & Geometric Topology (2021), in press.   pdf
2 citations by


A. Genevois, A. Stocker, Partially CAT(−1) groups are acylindrically hyperbolic, Bull. Soc. Math. France 147 (2019), no. 3, 377–394.
D. Gruber, A. Sisto, Infinitely presented graphical small cancellation groups are acylindrically hyperbolic, Ann. Inst. Fourier (Grenoble), 68 (2018), no. 6, 2501–2552.

[54] G.N. Arzhantseva, S. Gal, On approximation properties of semidirect products of groups,
Annales mathematiques Blaise Pascal, 27(1) (2020), 125-130.   pdf
5 citations by


F. Berlai, Residual properties of free products, Comm. Algebra 44 (2016), no. 7, 2959-2980.
A. Bhattacharya, M. Brannan, A. Chirvasitu, S. Wang, Property (T), property (F) and residual finiteness for discrete quantum groups, J. Noncommut. Geom. 14 (2020), no. 2, 567-589.
L. Bowen, P. Burton, Locally compact sofic groups, (2021), arXiv:2106:09118.
M. Doucha, J. Gismatullin, On Dual surjunctivity and applications, (2020), arXiv:2008:10565.
D. F. Holt, S. Rees, Some closure results for C-approximable groups, Pacific J. Math. 287 (2017), no. 2, 393-409.

[53] G.N. Arzhantseva, F. Berlai, M. Finn-Sell, L. Glebsky, Unrestricted wreath products and sofic groups,
International Journal of Algebra and Computation, 29(02) (2019), 343-355.   pdf
4 citations by


L. Bowen, P. Burton, Locally compact sofic groups, (2021), arXiv:2106:09118.
J. Brude, R. Sasyk, Permanence properties of verbal products and verbal wreath products of groups, (2019), arXiv:1909.07800.
J. Brude, R. Sasyk, Metric approximations of unrestricted wreath products when the acting group is amenable, (2020), arXiv:2004.05735.
R. Ji, C. Ogle, B. Ramsey, Relative amenability and relative soficity, (2018), arXiv:1807.07600

[52] G.N. Arzhantseva, Ch. Cashen, Cogrowth for group actions with strongly contracting elements,
Ergodic Theory and Dynamical Systems, 40(7) (2020), 1738-1754.   pdf
2 citations by


I. Gekhtman, A. Levit, Critical exponents of invariant random subgroups in negative curvature, Geom. Funct. Anal. 29 (2019), no. 2, 411-439.
K. Matsuzaki, Y. Yabuki, J. Jaerisch, Normalizer, divergence type, and Patterson measure for discrete groups of the Gromov hyperbolic space, Groups Geom. Dyn. 14 (2020), no. 2, 369-411.

[51] G.N. Arzhantseva, L. Paunescu, Constraint metric approximations and equations in groups,
Journal of Algebra, 516 (2018), 329-351.   pdf
2 citations by


F. Fournier-Facio, Ultrametric analogues of Ulam stability of groups , (2021), arXiv:2105.00516
A. Ioana, Stability for product groups and property (τ), J. Algebra 516 (2018), J. Funct. Anal. 279 (2020), no. 9, 108729, 32 pp.

[50] G.N. Arzhantseva, C. Drutu, Geometry of infinitely presented small cancellation groups and quasi-homomorphisms,
Canadian Journal of Mathematics, 71(5) (2019), 997-1018.   pdf
5 citations by


M. Bradenbursky, Ś. Gal, J. Kędra, M. Marcinkowski, The cancellation norm and the geometry of bi-invariant word metrics, Glasg. Math. J. 58 (2016), no. 1, 153–176.
I. Chatterji, Introduction to the rapid decay property, Around Langlands correspondences, 53-72, Contemp. Math., 691, Amer. Math. Soc., Providence, RI, 2017.
D. Gruber, A. Sisto, Infinitely presented graphical small cancellation groups are acylindrically hyperbolic, Ann. Inst. Fourier (Grenoble) 68 (2018), no. 6, 2501-2552.
A. Martin, Complexes of groups and geometric small cancelation over graphs of groups, Bull. Soc. Math. France 145 (2017), no. 2, 193-223.
M. Sapir, The rapid decay property and centroids in groups, J. Topol. Anal. 7 (2015), no. 3, 513–541.

[49] G.N. Arzhantseva, Ch. Cashen, D. Gruber, D. Hume, Negative curvature in graphical small cancellation groups,
Groups, Geometry and Dynamics, 13(2) (2019), 579-632.   pdf
12 citations by


T. Aougab, M. G. Durham, S. J. Taylor, Pulling back stability with applications to Out(Fn) and relatively hyperbolic groups, J. Lond. Math. Soc. (2) 96 (2017), no. 3, 565-583.
Ch. Cashen, Morse subsets of CAT(0) spaces are strongly contracting, Geom. Dedicata 204 (2020), 311–314.
Ch. Cashen, J. Mackay, A metrizable topology on the contracting boundary of a group Trans. Amer. Math. Soc. 372 (2019), no. 3, 1555–1600.
M. Cordes, D. Hume, Stability and the Morse boundary J. Lond. Math. Soc. (2) 95 (2017), no. 3, 963–988.
R. Coulon, D. Gruber, Small cancellation theory over Burnside groups, Adv. Math. 353 (2019), 722–775.
I. Gekhtman, W. Yang, Counting conjugacy classes in groups with contracting elements , (2018), arXiv:1810.02969.
D. Gruber, A. Sisto, Infinitely presented graphical small cancellation groups are acylindrically hyperbolic Ann. Inst. Fourier (Grenoble) 68 (2018), no. 6, 2501–2552.
S. Han, Relative Hyperbolicity of graphical small cancellation groups , (2020), arXiv:2010.13528.
D. Hume, A. Sisto, Groups with no coarse embeddings into hyperbolic groups New York J. Math. 23 (2017), 1657–1670.
M. Incenerti-Medici, Comparing topologies on the Morse boundary and quasi-isometry invariance, Geom. Dedicata 212 (2021), 153-176.
W. Yang, Statistically convex-cocompact actions of groups with contracting elements, Int. Math. Res. Not. IMRN 2019, no. 23, 7259-7323.
W. Yang, Genericity of contracting elements in groups, Math. Ann. 376 (2020), no. 3-4, 823-861.

[48] G.N. Arzhantseva, R. Tessera, Admitting a coarse embedding is not preserved under group extensions,
International Mathematics Research Notices, 2019 (20) (2019), 6480-6498.   pdf
8 citations by


B. Braga, , Y. C. Chung, and K. Li, Coarse Baum-Connes conjecture and rigidity for Roe algebras, Journal of Functional Analysis 279 (2020), no. 9, 108728.
C. Bönicke, C. Dell’Aiera, Going-down functors and the Künneth formula for crossed products by étale groupoids, Transactions of the American Mathematical Society, 372 (2019), no. 11, 8159-8194.
K. Boucher, On non-amenable embeddable spaces in relation with free products, (2018), arXiv:1801.04889.
T. Delabie, A. Khukhro, Box spaces of the free group that neither contain expanders nor embed into a Hilbert space. Advances in Mathematics 336 (2018), 70-96.
J. Deng, The Novikov conjecture and extensions of coarsely embeddable groups, (2019), arXiv:1910.05381.
J. Deng, Q. Wang, G. Yu, The coarse Baum-Connes conjecture for certain extensions and relative expanders, (2021), arXiv:2102.10617.
G. Li, X. Wang, Remarks on strong embeddability for discrete metric spaces and groups, arXiv:1709.02522.
K. Li, J. Špakula, J. Zhang, Measured asymptotic expanders and rigidity for Roe algebras, (2020), arXiv:2010.10749.

[47] G.N. Arzhantseva, G.A. Niblo, N. Wright, J. Zhang, A characterization for asymptotic dimension growth,
Algebraic & Geometric Topology, 18 (2018), 493-524.   pdf
4 citations by


T. Davila, Decomposition complexity growth of finitely generated groups, (2019), arXiv:1902.08561.
T. Davila, Infinite-dimensional coarse geometry of groups and spaces, PhD thesis, 2020, University of Florida.
E. Fioravanti, Superrigidity of actions on finite rank median spaces, Adv. Math. 352 (2019), 1206–1252.
J. Wang, Z. Xie, G. Yu, Decay of scalar curvature on uniformly contractible manifolds with finite asymptotic dimension, (2021), arXiv:2101.11584.

[46] G.N. Arzhantseva, Ch. Cashen, D. Gruber, D. Hume, Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction,
Documenta Mathematica, 22 (2017), 1193-1224.   pdf
29 citations by


C. Abbott, J. Behrstock, M. G. Durham, Largest acylindrical actions and Stability in hierarchically hyperbolic groups, Trans. Amer. Math. Soc. Ser. B 8 (2021), 66-104.
T. Aougab, M. G. Durham, S. J. Taylor, Pulling back stability with applications to Out(Fn) and relatively hyperbolic groups J. Lond. Math. Soc. (2) 96 (2017), no. 3, 565-583.
A. Bartels, M. Bestvina, The Farrell-Jones conjecture for mapping class groups, Invent. Math. 215 (2019), no. 2, 651-712.
J. Beyrer, E. Fioravanti, Cross ratios and cubulations of hyperbolic groups, (2018), arXiv:1810.08087.
N. Brady, H. C. Tran, Divergence of finitely presented groups, (2020), arXiv:2002.03653.
N. Brady, H. C. Tran, Divergence of finitely presented subgroups of CAT(0) groups, (2020), arXiv:2012.15803.
Ch. Cashen, Quasi-isometries need not induce homeomorphisms of contracting boundaries with the Gromov product topology Anal. Geom. Metr. Spaces 4 (2016), no. 1, 278–281.
Ch. Cashen, Morse subsets of CAT(0) spaces are strongly contracting Geom. Dedicata 204 (2020), 311–314.
Ch. Cashen, J. Mackay, A metrizable topology on the contracting boundary of a group Trans. Amer. Math. Soc. 372 (2019), no. 3, 1555–1600.
M. Cordes, A survey on Morse boundaries & stability, (2017), arXiv:1704.07598.
M. Cordes, D. Hume, Stability and the Morse boundary J. Lond. Math. Soc. (2) 95 (2017), no. 3, 963–988.
C. Druţu, S. Mozes, M. Sapir, Corrigendum to "Divergence in lattices in semisimple Lie groups and graphs of groups'', Trans. Amer. Math. Soc. 370 (2018), no. 1, 749-754.
E. Fink, Morse geodesics in torsion groups, (2017), arXiv:1710.11191.
E. Fioravanti, Cross ratios on cube complexes and length-spectrum rigidity, PhD thesis, 2019, University of Oxford.
M. Incenerti-Medici, Comparing topologies on the Morse boundary and quasi-isometry invariance, Geom. Dedicata 212 (2021), 153-176.
M. Hagen, Large facing tuples and a strengthened sector lemma, (2020), arXiv:2005.09536.
L. Huang, B. Kleiner, S. Stadler, Morse quasiflats I, (2019), arXiv:1911.04656.
H. Kim, Stable subgroups and Morse subgroups in mapping class groups, Internat. J. Algebra Comput. 29 (2019), no. 5, 893-903.
S. C. Mousley, J. Russell, Hierarchically hyperbolic groups are determined by their Morse boundaries, (2018), arXiv:1801.04867.
D. Murray, Y. Qing, A. Zalloum, Sublinearly Morse geodesics in CAT(0) spaces: Lower divergence and hyperplane characterization, (2020), arXiv:2008.09199.
A. Pal, R. Pandey, Acylindrical hyperbolicity of subgroups, New York J. Math. 26 (2020), 1213-1231.
A. Pal, R. Pandey, Contracting boundary of a cusped space, (2020), arXiv:2012.08259.
A. Pal, S. Paul, Strongly contracting geodesics in a tree of spaces, (2019), arXiv:1904.09906.
Y. Qing, K. Rafi, G. Tiozzo, Sublinearly Morse boundary I: CAT(0) spaces, (2020), arXiv:1909.02096.
Y. Qing, K. Rafi, G. Tiozzo, Sublinearly Morse boundary II: Proper geodesic spaces, (2020), arXiv:2011.03481.
Y. Qing, A. Zalloum, Rank one isometries in sublinearly morse boundaries of CAT(0) groups, (2019), arXiv:1911.03296.
J. Russell, D. Spriano, H.C. Tran, Convexity in hierarchically hyperbolic spaces, (2018), arXiv:1809.09303.
J. Russell, D. Spriano, H.C. Tran, The local-to-global property for Morse quasi-geodesics, (2019), arXiv:1908.11292.
H. C. Tran, On strongly quasiconvex subgroups, Geom. Topol. 23 (2019), no. 3, 1173-1235.

[45] G.N. Arzhantseva, L. Paunescu, Linear sofic groups and algebras,
Transactions of the American Mathematical Society, 369 (2017), 2285-2310.   pdf
28 citations by


A. Anderson, M. Lupini, The Fraïssé limit of matrix algebras with the rank metric, (2017), arXiv:1712.04431.
J. Brude, R. Sasyk, Permanence properties of verbal products and verbal wreath products of groups, (2019), arXiv:1909.07800.
J. Brude, R. Sasyk, Metric approximations of unrestricted wreath products when the acting group is amenable, (2020), arXiv:2004.05735.
V. Capraro, M. Lupini, Introduction to sofic and hyperlinear groups and Connes' embedding conjecture, Lecture Notes in Mathematics 2136, Springer 2015.
T. Ceccherini-Silberstein, M. Coornaert, On sofic monoids , Semigroup Forum 89 (2014), no. 3, 546–570.
M. de Chiffre, Approximate representations of groups, PhD thesis, 2018, Technischen Universität Dresden.
M. Doucha, Metric topological groups: their metric approximation and metric ultraproducts, Groups Geom. Dyn. 12 (2018), no. 2, 615-636.
G. Elek, Convergence and limits of linear representations of finite groups, J. Algebra 450 (2016), 588-615.
G. Elek, Infinite dimensional representations of finite dimensional algebras and amenability, (2015), arXiv:1512.03959.
G. Elek, L. Grabowski, Almost commuting matrices with respect to the rank metric , (2017), arXiv:1708.05338
F. Fournier-Facio, Ultrametric analogues of Ulam stability of groups, (2021), arXiv:2105.00516.
L. Glebsky, Approximations of groups, characterizations of sofic groups, and equations over groups, J. Algebra 477 (2017), 147-162.
M. Gromov, Number of questions, 2014, http://www.ihes.fr/~gromov/PDF/Problems-marc6-11-2014.pdf
M. Gromov, Morse spectra, homology measures, spaces of cycles and parametric packing problems, Ann. of Math. Stud. 205 (2020), 141-205.
B. Hayes, A. W. Sale, Metric approximations of wreath products, Ann. Inst. Fourier (Grenoble) 68 (2018), no. 1, 423-455.
D. F. Holt, S. Rees, Some closure results for C-approximable groups, (2016), arXiv:1601.01836
A. Ivanov, Sofic metric groups and continuous logic, (2016), arXiv:1604.08446
A. Ivanov, Metric ultraproducts of finite groups with respect to some length functions, (2014), arXiv:1401.0857
A. Ivanov, Soficity and hyperlinearity for metric groups, Topology Appl. 235 (2018), 146-156.
A. Korchagin, MF-property for countable discrete groups, (2017), arXiv:1704.06906.
M. Lupini, An invitation to model theory and C*-algebras, Bull. Symb. Log. 25 (2019), no. 1, 34-100.
N. Nikolov, J. Schneider, A. Thom, Some remarks on finitarily approximable groups, J. Éc. polytech. Math. 5 (2018), 239-258.
L. M. Rivera, N. M. Veyna García, Aproximación métrica de grupos: una breve perspectiva, (2017), arXiv:1709.01202
J. Schneider, On ultraproducts of compact quasisimple groups, PhD thesis, 2021, Universität Leipzig.
A. Stolz, Linear approximation of groups and ultraproducts of compact simple groups, PhD thesis, 2013, Universität Leipzig.
A. Stolz, Properties of linearily sofic groups, (2013), arXiv:1309.7830.
A. Thom, Finitary approximations of groups and their applications, Proceedings of the ICM (2018).
S. Virili, A point-free approach to L-Surjunctivity and stable finiteness, (2014), arXiv:1410.164.
S. Virili, Group representations, algebraic dynamics and torsion theories, PhD thesis, 2014, Universitat Autònoma de Barcelona.

[44] G.N. Arzhantseva, Ch. Cashen, J. Tao, Growth tight actions,
Pacific Journal of Mathematics, 278(1) (2015), 1-49.   pdf
23 citations by


A. Broise-Alamichel, J. Parkkonen, F. Paulin, Equidistribution and counting under equilibrium states in negative curvature and trees, Applications to non-Archimedean Diophantine approximation. Progress in Mathematics, 329, Birkhäuser/Springer, 2019.
C. Cashen, J. Tao, Growth tight actions of product groups, Groups Geom. Dyn. 10 (2016), no. 2, 753-770.
M. Cordes, J.Russell, D. Spriano, A. Zalloum, Regularity of Morse geodesics and growth of stable subgroups, (2020), arXiv:2008.06379.
R. Coulon, R. Dougall, B. Schapria, S. Tapie, Twisted Patterson-Sullivan measures and applications to amenability and coverings, (2018), arXiv:1809.10881.
F. Dahmani, D. Futer, D. T. Wise, Growth of quasiconvex subgroups, Math. Proc. Cambridge Philos. Soc. 167 (2019), no. 3, 505-530.
S. Das, M. Mj, Controlled Floyd separation and non relatively hyperbolic groups, J. Ramanujan Math. Soc. 30 (2015), no. 3, 267-294.
I. Gekhtman, S. J. Taylor, G. Tiozzo, Counting problems in graph products and relatively hyperbolic groups, Israel J. Math. 237 (2020), no. 1, 311-371.
I. Gekhtman, W. Yang, Counting conjugacy classes in groups with contracting elements , (2018), arXiv:1810.02969.
S. Gouëzel, C. Noûs, B. Schapira, S. Tapie, Pressure at infinity and strong positive recurrence in negativecurvature, (2020), arXiv:2007.08816v2.
J. Han, Growth of pseudo-anosov conjugacy classes in Teichmüller space, (2021), arXiv:2105.08640.
J. Han, Growth rate of dehn twist lattice points in Teichmüller space, (2021), arXiv:2105.08624.
S. Han, W. Yang, Generic free subgroups and statistical hyperbolicity, (2018), arXiv:1812.06265.
Z. He, J. Liu, W. Yang, Large quotients of group actions with a contracting element, (2020), arXiv:2007.15825.
I. Kapovic, J. Maher, C. Pfaff, S.J. Taylor, Random outer automorphisms of free groups: Attracting trees and their singularity structures, (2018), arXiv:1805.12382.
K. Matsuzaki, Growth and cogrowth tightnessof Kleinian and hyperbolic groups, RIMS Kôkyûroku Bessatsu B66 (2017), 21-36.
M. Mj, P. Roy, Stable random fields, Bowen-Margulis measures and extremal cocycle growth, (2018), arXiv:1809.08295v1.
Y. Qing, K. Rafi, G. Tiozzo, Sublinearly Morse boundary II: Proper geodesic spaces, (2020), arXiv:2011.03481.
K. Rafi, Y. Verberne, Geodesics in the mapping class group, (2018), arXiv:1810.12489.
J. Russell, D. Spriano, H.C. Tran, The local-to-global property for Morse quasi-geodesics, (2019), arXiv:1908.11292.
Y. Verberne, Pseudo-Anosov homeomorphisms constructed using poitive Dehn twists, PhD thesis, 2020, University of Toronto.
B. Wiest, Garside groups and geometry, (2020), arXiv:2008.08802.
W. Yang, Statistically convex-cocompact actions of groups with contracting elements, Int. Math. Res. Not. IMRN 2019, no. 23, 7259-7323.
W. Yang, Genericity of contracting elements in groups, Math. Ann. 376 (2020), no. 3-4, 823-861.

[43] G.N. Arzhantseva, L. Paunescu, Almost commuting permutations are near commuting permutations,
Journal of Functional Analysis, 269(3) (2015), 745-757.   pdf
34 citations by


S. Atkinson, Some results on tracial stability and graph products, (2018), arXiv:1808.04664.
S. Atkinson, S. Elayavalli, On ultraproduct embeddings and amenability for tracial von Neumann algebras, International Mathematics Research Notices (2021), no. 4, 2882-2918.
O. Becker, M. Chapman, Stability of approximate group actions: uniform and probabilistic, (2020), arXiv:2005.06652.
O. Becker, A. Lubotzky, Group stability and Property (T), J. Funct. Anal. 278 (2020), no. 1, 108298, 20 pp.
O. Becker, A. Lubotzky, J. Mosheiff, Testability of relations between permutations, (2020), arXiv:2011.05234.
O. Becker, A. Lubotzky, A. Thom, Stability and invariant random subgroups, Duke Math. J. 168 (2019), no. 12, 2207-2234.
O. Becker, J. Mosheiff, Abelian groups are polynomially stable, International Mathematics Research Notices (2020), 59pp.
L. Bowen, P. Burton, Flexible stability and nonsoficity, Trans. Amer. Math. Soc. 373 (2020), no. 6, 4469-4481.
V. Capraro, M. Lupini, Introduction to sofic and hyperlinear groups and Connes' embedding conjecture, Lecture Notes in Mathematics 2136, Springer 2015.
M. Cavaleri, Algorithms and quantifications in amenable and sofic groups, PhD thesis, Universita degli studi di Roma La Sapienza (2016).
M. Cavaleri, R. Munteanu, L. Paunescu, Two special subgroups of the universal sofic group, Ergodic Theory Dynam. Systems 39 (2019), no. 12, 3250-3261.
M. De Chiffre, Approximate representations of groups, PhD thesis, Technische Universität Dresden (2019).
M. De Chiffre, L. Glebsky, A. Lubotzky, A. Thom, Stability, cohomology vanishing, and non-approximable groups, Forum Math. Sigma 8 (2020), Paper No. e18, 37 pp.
S. Eilers, T. Shulman, A. Sørensen, C*-stability of discrete groups, Adv. Math. 373 (2020), 107324, 41 pp.
G. Elek, Ł. Grabowski, Almost commuting matrices with respect to the rank metric, (2021), arXiv:1708.05338v3.
D. Enders, T. Shulman, Almost commuting matrices, cohomology, and dimension, (2019), arXiv:1902.10451.
F. Fournier-Facio, Ultrametric analogues of Ulam stability of groups, (2021), arXiv:2105.00516.
M. A. García Morales, L. Glebsky, Property of defect diminishing and stability, (2019), arXiv:1911.11752v2.
D. Hadwin, T. Shulman, Stability of group relations under small Hilbert-Schmidt perturbations, J. Funct. Anal. 275 (2018), no. 4, 761–792.
D. Hadwin, T. Shulman, Variations of projectivity for C*-algebras, Pacific J. Math. 301 (2019), no. 2, 421-440.
H. Helfgott, K. Juschenko, Soficity, short cycles, and the Higman group, Trans. Amer. Math. Soc. 371 (2019), no. 4, 2771–2795.
A. Ioana, Stability for product groups and property (τ), J. Funct. Anal. 279 (2020), no. 9, 108729, 32 pp.
A. Ioana, On sofic approximations of F2×F2, Ergodic Theory and Dynamical Systems (2021), 1-19.
M. Kassabov, V. Kuperberg, T. Riley, Soficity and variations on Higman’s group, J. Comb. Algebra 3 (1) (2019), 41–70.
J. König, A. Leitner, D. Neftin, Almost-regular dessins d'enfant on a torus and sphere, Topology Appl. 243 (2018), 78–99.
N. Lazarovich, A. Levit, Y. Minsky, Surface groups are flexibly stable, (2019), arXiv:1901.07182.
A. Levit, A. Lubotzky, Infinitely presented stable groups and invariant random subgroups of metabelian groups, Ergodic Theory and Dynamical Systems (2021), 1-36.
A. Levit, A. Lubotzky, Uncountably many permutation stable groups, (2019), arXiv:1910.11722v1.
A. Lubotzky, I. Oppenheim, Non p-norm approximated groups, J. Anal. Math. 141 (2020), no. 1, 305-321.
M. Lupini, An invitation to model theory and C*-algebras, Bull. Symb. Log. 25 (2019), no. 1, 34–100.
R. Moreno, L.M. Rivera, Blocks in cycles and k-commuting permutations, SpringerPlus (2016) 5: 1949.
L. Oppenheim, Garland's method with Banach coefficients, (2020), arXiv:2009.01234.
L. Paunescu, F. Radulescu, A generalisation to Birkhoff-von Neumann theorem, Adv. Math. 308 (2017), 836-858.
L. M. Rivera, Integer sequences and k-commuting permutations, Integers 15 (2015), Paper No. A46, 22 pp.

[42] G.N. Arzhantseva, D. Osajda, Infinitely presented small cancellation groups have Haagerup property,
Journal of Topology and Analysis, 7(3) (2015), 389-406.   pdf
12 citations by


V. Alekseev, M. Finn-Sell, Sofic boundaries of groups and coarse geometry of sofic approximations, Groups Geom. Dyn. 13 (2019), no. 1, 191-234.
P. Baum, E. Guentner, R. Willett, Exactness and the Kadison-Kaplansky conjecture, Operator algebras and their applications, 1-33, Contemp. Math., 671, Amer. Math. Soc., Providence, RI, 2016.
Y. Cornulier, Group actions with commensurated subsets, wallings and cubings, (2013), arXiv:1302.5982v2.
M. Finn-Sell, Almost quasi-isometries and more non-exact groups, Math. Proc. Cambridge Philos. Soc. 162 (2017), no. 3, 393-403.
F. Fournier-Facio, Ultrametric analogues of Ulam stability of groups, (2021), arXiv:2105.00516.
D. Gruber, Infinitely presented C(6)-groups are SQ-universal, J. Lond. Math. Soc. (2) 92 (2015), no. 1, 178-201.
D. Gruber, A. Sisto, Infinitely presented graphical small cancellation groups are acylindrically hyperbolic, Ann. Inst. Fourier (Grenoble) 68 (2018), no. 6, 2501-2552.
S. Knudby, On connected Lie groups and the approximation property, C. R. Math. Acad. Sci. Paris 354 (2016), no. 7, 697-699.
A. Martin, Complexes of groups and geometric small cancellation over graphs of groups, Bull. Soc. Math. France 145 (2017), no. 2, 193-223.
M. Mimura, Amenability versus non-exactness of dense subgroups of a compact group. J. Lond. Math. Soc. (2) 100 (2019), no. 2, 592-622.
M. Mimura, H. Sako, Group approximation in Cayley topology and coarse geometry, Part II: Fibred coarse embeddings, Anal. Geom. Metr. Spaces 7 (2019), no. 1, 62-108.
D. Osajda, Small cancellation labellings of some infinite graphs and applications, Acta Math. 225 (2020), no. 1, 159-191.

[41] G.N. Arzhantseva, R. Tessera, Relative expanders,
Geometric and Functional Analysis [GAFA], 25(2) (2015), 317-341.   pdf
17 citations by


P. Awasthi, M. Charikar, R. Krishnaswamy, and A. K. Sinop, Spectral Embedding of k-Cliques, Graph Partitioning and k-Means, In Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science (ITCS '16). Association for Computing Machinery, New York, NY, USA, 301–310.
C. Cave, On coarse geometric properties of discrete andlocally compact groups, PhD thesis, 2015, University of Southampton.
K. Das, From the geometry of box spaces to the geometry and measured couplings of groups, J. Topol. Anal. 10 (2018), no. 2, 401-420.
T. Delabie, Large scale geometry of box spaces, PhD thesis, 2018, Université de Neuchâtel.
T. Delabie, A. Khukhro, Box spaces of the free group that neither contain expanders nor embed into a Hilbert space, Adv. Math. 336 (2018), 70-96.
J. Deng, Q. Wang, G. Yu, The coarse Baum-Connes conjecture for certain extensions and relative expanders, (2021), arXiv:2102.10617.
A. Eskenazis, Geometric inequalities and advances in the Ribe program, PhD thesis, 2019, Princeton University.
A. Eskenazis, M. Mendel, A. Naor, Nonpositive curvature is not coarsely universal, Invent. Math. 217 (2019), no. 3, 833-886.
D. Hume, A continuum of expanders, (2014), Fund. Math. 238 (2017), no. 2, 143-152.
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K. Li, J. Špakula, J. Zhang, Measured asymptotic expanders and rigidity for Roe algebras, (2020), arXiv:2010.10749.
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A.V. Borovik, A.G. Myasnikov, V.N. Remeslennikov, Multiplicative measures on free groups, Internat. J. Algebra Comput. 13 (2003), no. 6, 705-731.
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J. Delgado Rodríguez, Extensions of free groups: algebraic, geometric, and algorithmic aspects, PhD thesis, 2017, Universitat Politècnica Catalunya.
R. Gilman, A. Myasnikov, V. Roman'kov, Random equations in nilpotent groups, J. Algebra 352 (2012), 192–214.
J. Friedman, Sheaves on graphs, their homological invariants, and a proof of the Hanna Neumann conjecture: with an appendix by Warren Dicks, Mem. Amer. Math. Soc. 233 (2015), no. 1100, xii+106 pp.
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V. Kaimanovich, I. Kapovich, P. Schupp, The subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007), 1-46.
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Average-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343-359.
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694.
I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119.
I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404.
I. Kapovich, P. Schupp, V. Shpilrain, Generic properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), no. 1, 113-140.
I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933.
I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19.
I. Kapovich, P. Schupp, Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113.
O. Kharlampovich, A. Myasnikov, P. Weil, Stallings graphs for quasi-convex subgroups, J. Algebra 488 (2017), 442–483.
O. Kharlampovich, P. Weil, On the generalized membership problem in relatively hyperbolic groups, Fields of logic and computation. III, 147–155, Lecture Notes in Comput. Sci., 12180, Springer, Cham, 2020.
S. Margolis, J. Meakin, Z. Sunik, Distortion functions and the membership problem for submonoids of groups and monoids, Geometric methods in group theory, 109-129, Contemp. Math., 372, Amer. Math. Soc., Providence, RI, 2005.
Y. Ollivier, A January 2005 invitation to random groups, Ensaios Matemáticos, 10. Sociedade Brasileira de Matemática, Rio de Janeiro, 2005. ii+100 pp.
M. Sapir, Asymptotic invariants, complexity of groups and related problems, Bull. Math. Sci. 1 (2011), no. 2, 277–364.
M. Shusterman, P. Zalesskii, Virtual retraction and Howson's theorem in pro-p groups Trans. Amer. Math. Soc. 373 (2020), no. 3, 1501–1527.
B. Solie, Genericity of filling elements, Internat. J. Algebra Comput. 22 (2012), no. 2, 1250008, 10 pp.
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I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694.
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I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933.
I. Kapovich, P. Schupp, Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113.
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F. Bassino, A. Martino, C. Nicaud, P. Weil, Random presentations and random subgroups: a survey, (2017), arXiv:1702.01942.
F. Bassino, A. Martino, C. Nicaud, E. Ventura, P. Weil, Statistical properties of subgroups of free groups, Random Structures Algorithms 42 (2013), no. 3, 349–373.
F. Bassino, C. Nicaud, P. Weil, On the genericity of Whitehead minimality, J. Group Theory 19 (2016), no. 1, 137–159.
F. Bassino, C. Nicaud, P. Weil, Generic properties of subgroups of free groups and finite presentations, Algebra and Computer Science, 677, American Mathematical Society, pp.1-44, 2016. Contemporary Mathematics.
F. Bassino, C. Nicaud, P. Weil, Silhouettes and generic properties of subgroups of the modular group, (2020), arXiv:2011.09179.
G. Bergman, On monoids, 2-firs, and semifirs, Semigroup Forum 89 (2014), no. 2, 293–335.
A. Bishop, M. Ferov, Density of metric small cancellation in finitely presented groups, J. Groups Complex. Cryptol. 12 (2020), no. 2, Paper No. 1, 18 pp.
R. Brown, J. Nan, Stabilizers of fixed point classes and Nielsen numbers of n-valued maps, Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 4, 523–535.
I. Bumagin, On small cancellation k-generated groups with (k-1)-generated subgroups all free, Internat. J. Algebra Comput. 11 (2001), no. 5, 507-524.
A. Carnevale, M. Cavaleri, Partial word and equality problems and Banach densities, Adv. Math. 368 (2020), 107133, 16 pp.
Ch. Cashen, J. Manning, Virtual geometricity is rare, LMS J. Comput. Math. 18 (2015), no. 1, 444–455.
M. Cavaleri, Følner functions and the generic word problem for finitely generated amenable groups, J. Algebra 511 (2018), 388–404.
T. Ceccherini-Silberstein, A. Samet-Vaillant, Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint, Functional analysis. J. Math. Sci. (N.Y.) 156 (2009), no. 1, 56–108.
S. Cleary, M. Elder, A. Rechnitzer, J. Taback, Random subgroups of Thompson's group F, Groups Geom. Dyn. 4 (2010), no. 1, 91–126.
P. Dani, I. Levcovitz, Subgroups of right-angled Coxeter groups via Stallings-like techniques, (2019), arXiv:1908.09046.
E. Frenkel, A.G. Myasnikov, V.N. Remeslennikov, Regular sets and counting in free groups, (2009), arXiv:0906.2850.
I. Gekhtman, S. Taylor, G. Tiozzo, Counting loxodromics for hyperbolic actions, J. Topol. 11 (2018), no. 2, 379–419.
I. Gekhtman, S. Taylor, G. Tiozzo, Counting problems in graph products and relatively hyperbolic groups, Israel J. Math. 237 (2020), no. 1, 311–371.
E. Ghys, Random groups (following Misha Gromov, ...), Astérisque No. 294 (2004), viii, 173-204.
R. Gilman, A. Miasnikov, D. Osin, Exponentially generic subsets of groups, Illinois J. Math. 54 (2010), no. 1, 371–388.
R. Gilman, A. Myasnikov, V. Roman'kov, Random equations in nilpotent groups, J. Algebra 352 (2012), 192–214.
N. Gupta, I. Kapovich, The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces. With an appendix by Khalid Bou-Rabee, Math. Proc. Cambridge Philos. Soc. 166 (2019), no. 1, 83–121.
L. Guyot, Estimating Minkowski dimensions in the space of marked groups, Ann. Fac. Sci. Toulouse Math. (6) 16 (2007), no. 1, 107-124.
P. de la Harpe, Uniform growth in groups of exponential growth, Geom. Dedicata 95 (2002), 1-17.
A. Juhász, A Freiheitssatz for Whitehead graphs of one-relator groups with small cancellation, Comm. Algebra 37 (2009), no. 8, 2714–2741.
V. Kaimanovich, I. Kapovich, P. Schupp, The subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007), 1-46.
I. Kapovich, On mathematical contributions of Paul E. Schupp, Illinois J. Math. 54 (2010), no. 1, 1–9.
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Average-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343-359.
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694.
I. Kapovich, I. Rivin, P. Schupp, V. Shpilrain, Densities in free groups and Zk, visible points and test elements, Math. Res. Lett. 14 (2007), no. 2, 263-284.
I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119.
I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404.
I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933.
I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19.
I. Kapovich, P. Schupp, Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113.
I. Kapovich, P. Schupp, V. Shpilrain, Generic properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), no. 1, 113-140.
I. Kapovich, R. Weidmann, Kleinian groups and the rank problem, Geom. Topol. 9 (2005), 375-402.
I. Kapovich, R. Weidmann, Freely indecomposable groups acting on hyperbolic spaces, Internat, J. Algebra Comput. 14 (2004), no. 2, 115-171.
I. Kapovich, R. Weidmann, Nielsen equivalence in a class of random groups, J. Topol. 9 (2016), no. 2, 502–534.
O. Kharlampovich, A. Myasnikov, P. Weil, Stallings graphs for quasi-convex subgroups, (2014), arXiv:1408.1917.
O. Kharlampovich, P. Weil, On the generalized membership problem in relatively hyperbolic groups, Fields of logic and computation. III, 147–155, Lecture Notes in Comput. Sci., 12180, Springer, Cham, 2020.
S. Kim, Ch. Staecker, Dynamics of random selfmaps of surfaces with boundary, Discrete Contin. Dyn. Syst. 34 (2014), no. 2, 599–611.
I. Kozakov, Percolation and Ising model on graphs with tree-like structure, (2008), PhD thesis, Vanderbilt University.
Y. Liu, M. M. Wood, The free group on n generators modulo n+u random relations as n goes to infinity, J. Reine Angew. Math. 762 (2020), 123–166.
L. Louder, H. Wilton, Negative immersions for one-relator groups, (2018), arXiv:1803.02671.
J. Mackay, Conformal dimension and random groups, Geom. Funct. Anal. 22 (2012), no. 1, 213–239.
J. Maher, A. Sisto, Random subgroups of acylindrically hyperbolic groups and hyperbolic embeddings, Int. Math. Res. Not. IMRN 2019, no. 13, 3941–3980.
A. Mann, How groups grow, London Mathematical Society Lecture Note Series, 395. Cambridge University Press, Cambridge, 2012. x+199 pp.
S. Margolis, J. Meakin, Z. Sunik, Distortion functions and the membership problem for submonoids of groups and monoids, Geometric methods in group theory, 109-129, Contemp. Math., 372, Amer. Math. Soc., Providence, RI, 2005.
L. Markus-Epstein, Stallings foldings and subgroups of amalgams of finite groups, Internat. J. Algebra Comput. 17 (2007), no. 8, 1493-1535.
A. Myasnikov, V. Shpilrain, A. Ushakov, Group-based cryptography, Birkhäuser, 2008.
Y. Ollivier, Sharp phase transition theorems for hyperbolicity, Geom. Funct. Anal. 14 (2004), no. 3, 595-679.
Y. Ollivier, Critical densities for random quotients of hyperbolic groups, C. R. Math. Acad. Sci. Paris 336 (2003), no. 5, 391-394.
Y. Ollivier, A January 2005 invitation to random groups, Ensaios Matemáticos, 10. Sociedade Brasileira de Matemática, Rio de Janeiro, 2005. ii+100 pp.
M. Sapir, Asymptotic invariants, complexity of groups and related problems, Bull. Math. Sci. 1 (2011), no. 2, 277–364.
P. Schupp, Coxeter groups, 2-completion, perimeter reduction and subgroup separability, Geom. Dedicata 96 (2003), 179-198.
V. Shpilrain, Average-case complexity of the Whitehead problem for a free group, (2021), arXiv:2105.01366.
I. Snopce, S. Tanushevski, Asymptotic density of test elements in free groups and surface groups, Int. Math. Res. Not. IMRN 2017, no. 18, 5577–5590.
B. Solie, Genericity of filling elements, Internat. J. Algebra Comput. 22 (2012), no. 2, 1250008, 10 pp.
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M. Steenbock, Rips-Segev torsion-free groups without the unique product property, J. Algebra 438 (2015), 337–378.
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D. T. Wise, An Invitation to Coherent Groups. What's Next?, edited by Dylan Thurston, Princeton: Princeton University Press, 2020, pp. 326-414.

[17] G.N. Arzhantseva, Generic properties of finitely presented groups,
PhD thesis, Moscow Lomonosov State University, December 1998.

Books (edited):

[16] G.N. Arzhantseva, A.Valette (eds.), Limits of graphs in group theory and computer science, ,
Fundamental Sciences, EPFL Press, Lausanne, 2009, 305 pp.     book

[15] G.N. Arzhantseva, L. Bartholdi, J. Burillo, and E. Ventura (eds.), Geometric group theory, ,
Fundamental Sciences, EPFL Press, Lausanne, 2009, 305 pp.     book

Submitted papers and preprints:

[14] G.N. Arzhantseva, A. Biswas, Large girth graphs with bounded diameter-by-girth ratio, (2018), submitted.   pdf
8 citations by


I. Benjamini, M. Fraczyk, G. Kun, Expander spanning subgraphs with large girth, (2020), arXiv:2012.15502.
A. Biswas, Flexibility and movability in Cayley graphs, (2019), arXiv:1911.06261.
A. Biswas, J. P. Saha, Expansion in Cayley graphs, Cayley sum graphs and their twists, (2021), arXiv:2103.05935.
T. Budzinski, N. Curien, B. Petri, On the minimal diameter of closed hyperbolic surfaces, Duke Math. J. 170(2) (2021), 365-377.
A. S. Detinkoa, W. A. de Graaf, 2-Generation of simple Lie algebras and free dense subgroups of algebraic groups, Journal of Algebra 545 (2020), 159-173.
D. Gruber, A. Sisto, Divergence and quasi-isometry classes of random Gromov's monsters, (2018), arXiv:1805.04039.
M. W. Liebeck, A. Shalev, Girth, words and diameter, Bull. London Math. Soc. 51 (2019), no. 3, 539-546.
M. Zeggel, The bounded isomorphism conjecture for box spaces of residually finite groups, (2021), arXiv:2103.16967.

[13] G.N. Arzhantseva, M. Steenbock, Rips construction without unique product, (2014), submitted.   pdf
10 citations by


N. Dunbfield, S. Kionke, J. raimbault, On geometric aspects of diffuse groups, (2017), https://hal.archives-ouvertes.fr/hal-01593698/document.
M. Finn-Sell, Almost quasi-isometries and more non-C*-exact groups, Mathematical Proceedings of the Cambridge Philosophical Society 162 (2017), no. 3, pp. 393-403.
G. Gardam, A counterexample to the unit conjecture for group rings, (2021), arXiv:2102.11818.
D. Gruber, Infinitely presented C(6)-groups are SQ-universal, J. Lond. Math. Soc. (2) 92 (2015), no. 1, 178-201.
D. Gruber, A. Martin, M. Steenbock, Finite index subgroups without unique product in graphical small cancellation groups, Bull. Lond. Math. Soc. 47 (2015), no. 4, 631–638.
D. Gruber, A. Sisto, Infinitely presented graphical small cancellation groups are acylindrically hyperbolic, Annales de l'Institut Fourier, Tome 68 (2018) no. 6, pp. 2501-2552.
K. Khan, Fundamental groups of certain von Neumann algebras, PhD thesis, (2020), Vanderbilt University.
K. Khan, Subgroups of Lacunary hyperbolic groups and free products, (2020), arXiv:2002.08540.
S. Kionke, J. Raimbault, N. Dunfield, On geometric aspects of diffuse groups, (2014), arXiv:1411.6449.
A. Martin, M. Steenbock, A combination theorem for cubulation in small cancellation theory over free products, (2014), arXiv:1409.3678.
J. Öinert, Units, zero-divisors and idempotents in rings graded by torsion-free groups, (2019), arXiv:1904.04847.

[12] G.N. Arzhantseva, D. Osajda, Graphical small cancellation groups with the Haagerup property, (2014).   pdf
14 citations by


V. Alekseev, M. Finn-Sell, Sofic boundaries of groups and coarse geometry of sofic approximations, (2016), arXiv.org:1608.02242.
P. Baum, E. Guentner, R. Willett, Exactness and the Kadison-Kaplansky conjecture, Operator algebras and their applications, 1-33, Contemp. Math., 671, Amer. Math. Soc., Providence, RI, 2016.
J. Deng, Q. Wang, G. Yu, The coarse Baum-Connes conjecture for certain extensions and relative expanders, (2021), arXiv:2102.10617.
M. Finn-Sell, Controlled analytic properties and the quantitive Baum-Connes Conjecture, (2019), arXiv:1908.02131.
D. Gruber, A. Sisto, Infinitely presented graphical small cancellation groups are acylindrically hyperbolic, (2014), arXiv:1411.7367.
S. Knudby, On connected Lie groups and the approximation property (2016), arXiv:1603.05518.
M. Mimura, Amenability versus non-exactness of dense subgroups of a compact group. J. Lond. Math. Soc. (2) 100 (2019), no. 2, 592-622.
M. Mimura, H. Sako, Group approximation in Cayley topology and coarse geometry, Part I: Coarse embeddings of amenable groups, Journal of Topology and Analysis 13 (2021), no. 1, 1–47.
M. Mimura, H. Sako, Group approximation in Cayley topology and coarse geometry, Part II: Fibred coarse embeddings, Anal. Geom. Metr. Spaces 7 (2019), no. 1, 62-108.
D. Osajda, Small cancellation labellings of some infinite graphs and applications, (2014), arXiv.org:1406.5015.
N. Ozawa, Y. Suzuki, On characterizations of amenable C*-dynamical systems and new examples, (2020), arXiv:2011.03420.
D. Sawicki, Warped cones over profinite completions, J. Topol. Anal. 10 (2018), no. 3, 563-584.
D. Sawicki, J. Wu, Straightening warped cones, Journal of Topology and Analysis (2020), 1-25.
Q. Wang, Y. Zhang, The coarse Novikov conjecture for extensions of coarsely embeddable groups, (2021), arXiv:2105.04753.

[11] G.N. Arzhantseva, C. Drutu, Geometry of infinitely presented small cancellation groups, Rapid Decay and quasi-homomorphisms, (2014).   pdf
5 citations by


M. Brandenbursky, S. Gal, J. Kędra, M. Marcinkowski, The cancellation norm and the geometry of bi-invariant word metrics, Glasg. Math. J. 58 (2016), no. 1, 153–176.
I. Chatterji, Introduction to the rapid decay property, (2016), arXiv:1604.06387.
D. Gruber, A. Sisto, Infinitely presented graphical small cancellation groups are acylindrically hyperbolic, (2014), arXiv:1408.4488
A. Martin, Complexes of groups and geometric small cancellation over graphs of groups, (2013), arXiv:1306.6847v2.
M. Sapir, The rapid decay property and centroids in groups, J. Topol. Anal. 7 (2015), no. 3, 513–541.

[10] G.N. Arzhantseva and T. Delzant, Examples of random groups, (2008).
first version (October 28, 2008), revised version (August 26, 2011).   pdf
74 citations by


A. Bartels, W. Lueck, The Borel conjecture for hyperbolic and CAT(0)-groups, Ann. of Math. (2) 175 (2012), no. 2, 631–689.
M. Bestvina, V. Guirardel, C. Horbez, Boundary amenability of Out(FN) , (2017), arXiv:1705.07017.
P. Baum, Dirac operator and K-theory for discrete groups. A celebration of the mathematical legacy of Raoul Bott, 97–107, CRM Proc. Lecture Notes, 50, Amer. Math. Soc., Providence, RI, 2010.
P. Baum, E. Guentner, R. Willett, Exactness and the Kadison-Kaplansky conjecture, Operator algebras and their applications, 1-33, Contemp. Math., 671, Amer. Math. Soc., Providence, RI, 2016.
P. Baum, E. Guentner, R. Willett, Expanders, exact crossed products, and the Baum-Connes conjecture, (2013), arXiv:1311.2343.
J. Brodzki, Ch. Cave, K. Li, Exactness of locally compact groups, Adv. Math. 312 (2017), 209–233.
M. Cordes, D. Hume, Stability and the Morse boundary, J. Lond. Math. Soc. (2) 95 (2017), no. 3, 963–988.
Y. de Cornulier, Y. Stalder, A. Valette, Proper actions of wreath products and generalizations, Trans. Amer. Math. Soc. 364 (2012), no. 6, 3159–3184.
R. Coulon, Asphericity and small cancellation theory for rotation families of groups, Groups Geom. Dyn. 5 (2011), no. 4, 729–765.
R. Coulon, Automorphismes extérieurs du groupe de Burnside libre, PhD thesis, University of Strasbourg, 2010.
R. Coulon, On the geometry of Burnside quotients of torsion free hyperbolic groups. Internat. J. Algebra Comput. 24 (2014), no. 3, 251–345.
R. Coulon, Théorie de la petite simplification: une approche géométrique [d'après F. Dahmani, V. Guirardel, D. Osin et S. Cantat, S. Lamy], (French) [Small cancellation theory: a geometric approach (after F. Dahmani, V. Guirardel, D. Osin, and S. Cantat, S. Lamy)] Astérisque No. 380, Séminaire Bourbaki. Vol. 2014/2015 (2016), Exp. No. 1089, 1–33.
R. Coulon, D. Gruber, Small cancellation theory over Burnside groups, (2017), arXiv:1705.09651.
R. Coulon, M. Hull, C. Kent, A Cartan-Hadamard type result for relatively hyperbolic groups, Geom. Dedicata 180 (2016), 339–371.
F. Dahmani, V. Guirardel, D. Osin, Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces, Mem. Amer. Math. Soc. 245 (2017), no. 1156, v+152 pp.
T. Delabie, A. Khukhro, Box spaces of the free group that neither contain expanders nor embed into a Hilbert space. Advances in Mathematics 336 (2018), 70-96.
T. Delabie, M. Tointon, The asymptotic dimension of box spaces of virtually nilpotent groups, Discrete Math. 341 (2018), no. 4, 1036–1040.
T. Deprez, Ozawa's class S for locally compact groups and unique prime factorization, (2019), arXiv:1904.02090.
A. Dranishnikov, M. Zarichnyi, Asymptotic dimension, decomposition complexity, and Haver's property C, Topology Appl. 169 (2014), 99–107.
C. Druţu, M. Kapovich, Geometric group theory, With an appendix by Bogdan Nica. American Mathematical Society Colloquium Publications, 63. American Mathematical Society, Providence, RI, 2018. xx+819 pp.
A. Eskenazis, Geometric inequalities and advances in the Ribe program, PhD thesis, 2019, Princeton University.
A. Eskenazis, M. Mendel, A. Naor, Nonpositive curvature is not coarsely universal, Invent. Math. 217 (2019), no. 3, 833-886.
M. Finn-Sell, Almost quasi-isometries and more non-C*-exact groups, Math. Proc. Cambridge Philos. Soc. 162 (2017), no. 3, 393–403.
M. Finn-Sell, Controlled analytic properties and the quantitive Baum-Connes Conjecture, (2019), arXiv:1908.02131.
M. Finn-Sell, On the Baum-Connes conjecture for Gromov monster groups, (2014), arXiv:1401.6841.
M. Gerasimova, D. Gruber, N. Monod, A. Thom, Asymptotics of Cheeger constants and unitarisability of groups, (2018), arXiv:1801.09600.
M. P. Gomez Aparicio, P. Julg, A. Valette, The Baum–Connes conjecture: an extended survey, In Advances in Noncommutative Geometry (pp. 127-244), 2019, Springer, Cham.
D. Gruber, Infinitely presented C(6)-groups are SQ-universal, J. Lond. Math. Soc. (2) 92 (2015), no. 1, 178–201.
D. Gruber, Groups with graphical C(6) and C(7) small cancellation presentations, Trans. Amer. Math. Soc. 367 (2015), no. 3, 2051–2078.
D. Gruber, A. Sisto, Infinitely presented graphical small cancellation groups are acylindrically hyperbolic , Ann. Inst. Fourier (Grenoble) 68 (2018), no. 6, 2501–2552.
D. Gruber, A. Sisto, Divergence and quasi-isometry classes of random Gromov's monsters, (2018), arXiv:1805.04039.
D. Gruber, A. Sisto, R. Tessera, Random Gromov's monsters do not act non-elementarily on hyperbolic spaces, Proc. Amer. Math. Soc. 148 (2020), no. 7, 2773–2782.
E. Guentner, R. Tessera, G. Yu, A notion of geometric complexity and its application to topological rigidity, arxiv:1008.0884v1.
E. Guentner, R. Tessera, G. Yu, Discrete groups with finite decomposition complexity, Groups Geom. Dyn. 7 (2013), no. 2, 377–402.
V. Guirardel, Geometric small cancellation, Geometric group theory, 55–90, IAS/Park City Math. Ser., 21, Amer. Math. Soc., Providence, RI, 2014.
S. Han, Relative hyperbolicity of graphical small cancellation groups , (2020), arXiv:2010.13528.
D. Hume, Direct embeddings of relatively hyperbolic groups with optimal ℓp compression exponent, J. Reine Angew. Math. 703 (2015), 147–172.
D. Hume, Separation profiles, coarse embeddability and inner expansion, (2014), arXiv:arXiv:1410.0246v1.
C. Horbez, J. Huang, Boundary amenability and measure equivalence rigidity among two-dimensional Artin groups of hyperbolic type, (2020), arXiv:2004.09325.
H. Izeki, T. Kondo, Sh. Nayatani, N-step energy of maps and the fixed-point property of random groups, Groups Geom. Dyn. 6 (2012), no. 4, 701–736.
R. Kasilingam, Topological rigidity problems, (2015), arXiv:1510.04139.
A. Khukhro, Espaces et groupes non exacts admettant un plongement grossier dans un espace de Hilbert, Séminaire Bourbaki 71e année, 2018-2019, no. 1154.
M. Kotowski, Gromov's random group, (2013), notes, https://www.mimuw.edu.pl/~mk249019/notes-01-03-2013.pdf.
V. Lafforgue, Conjecture de Baum-Connes, théorie de Fonataine en caractéristique p, et programme de Langlands géométriques, (2009), Habilitation thesis, University of Paris 7.
W. Lueck, Survey on aspherical manifolds, European Congress of Mathematics, 53–82, Eur. Math. Soc., Zürich, 2010.
W. Lueck, Aspherical manifolds, Bulletin of the Manifold Atlas 2012, 1-17.
W. Lueck, Some open problems about aspherical closed manifolds, (2014) In: Ancona V., Strickland E. (eds) Trends in Contemporary Mathematics. Springer INdAM Series, vol 8. Springer, Cham.
W. Lueck, K- and L-theory of group rings, (2010), arXiv:1003.5002v1.
W. Lueck, Isomorphism conjectures in K- and L-theory, 2021, http://www.him.uni-bonn.de/lueck/data/ic.pdf.
M. Mimura, Amenability versus non-exactness of dense subgroups of a compact group. J. Lond. Math. Soc. (2) 100 (2019), no. 2, 592-622.
M. Mimura, H. Sako, Group approximation in Cayley topology and coarse geometry, Part I: Coarse embeddings of amenable groups, Journal of Topology and Analysis 13 (2021), no. 1, 1–47.
A. Naor, L. Silberman, Poincaré inequalities, embeddings, and wild groups, Compos. Math. 147 (2011), no. 5, 1546–1572.
S. Nayatani, Fixed‐point property for affine actions on a Hilbert space, RIMS Kôkyûroku Bessatsu B66 (2017), 115−131.
P. Nowak, G. Yu, Large-Scale geometry, (2010), EMS publishing house, to appear. http://www.math.tamu.edu/~pnowak/book_etb/book_etb.pdf.
P. Nowak, Group actions on Banach spaces, Handbook of group actions. Vol. II, 121–149, Adv. Lect. Math. (ALM), 32, Int. Press, Somerville, MA, 2015.
Y. Ollivier, A January 2005 invitation to random groups, Ensaios Matemáticos [Mathematical Surveys], 10. Sociedade Brasileira de Matemática, Rio de Janeiro, 2005. ii+100 pp.
D. Osajda, Small cancellation labellings of some infinite graphs and applications, Acta Math. 225 (2020), no. 1, 159-191.
G. Pisier, Interpolation and Fatou-Zygmund property for completely Sidon subsets of discrete groups (New title: Completely Sidon sets in discrete groups), (2017), arXiv:1706.03844.
G. Pisier, Tensor products of C*-algebras and operator spaces, London Mathematical Society student texts 96, Cambridge, New York, Cambridge University Press, 2020, x+484 pp.
M. Puschnigg, The Baum-Connes conjecture with coefficients for word-hyperbolic groups, (after Vincent Lafforgue). Astérisque No. 361 (2014), Exp. No. 1062, vii, 115–148.
M. Sapir, A Higman embedding preserving asphericity, J. Amer. Math. Soc. 27 (2014), no. 1, 1–42.
M. Sapir, Aspherical groups and manifolds with extreme properties, (2011), arXiv:1103.3873v3.
M. Sapir, Asymptotic invariants, complexity of groups and related problems, Bull. Math. Sci. 1 (2011), no. 2, 277–364.
D. Sawicki, J. Wu, Straightening warped cones, (2017), arXiv:1705.06725.
J. Špakula, R. Willett, On rigidity of Roe algebras, Adv. Math. 249 (2013), 289–310.
F. Vigolo, Geometry of actions, expanders and warped cones, PhD thesis, 2018, University of Oxford.
Sh. Weinberger, G. Yu, Finite part of operator K-theory for groups finitely embeddable into Hilbert space and the degree of nonrigidity of manifolds, Geom. Topol. 19 (2015), no. 5, 2767–2799.
S. White, R. Willett, Cartan subalgebras in uniform Roe algebras, Groups Geom. Dyn. 14 (2020), no. 3, 949–989.
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[9] G.N. Arzhantseva, P.-A. Cherix, Quantifying metric approximations of discrete groups,
preprint, University of Geneva, (2008), revised version (2020), submitted.   pdf
4 citations by


H. Bradford, Quantifying local embeddings into finite groups, (2021), arXiv:2104.07111.
H. Bradford, D. Dona, Topological full groups of minimal subshifts and quantifying local embeddings into finite groups, (2021), arXiv:2106.09145.
F. Fournier-Facio, Ultrametric analogues of Ulam stability of groups , (2021), arXiv:2105.00516.
A. Ivanov, Sofic profiles of S(ω) and computability, Arch. Math. Logic 60 (2021), no. 3-4, 477–494.

[8] G.N. Arzhantseva, An algorithm detecting Dehn presentations,
preprint, University of Geneva, (2000).   pdf
3 citations by


A. Darbinyan, The word and conjugacy problems in lacunary hyperbolic groups, (2017), arXiv:1708.04591.
V. Diekert, A. Duncan, A. Myasnikov, Geodesic rewriting systems and pregroups, (2009), arXiv.org:0906.2223.
O. Kharlampovich, A. Myasnikov, P. Weil, Stallings graphs for quasi-convex subgroups (2014), arXiv:1408.1917.

Papers in Theoretical Computer Science/Applied mathematics (refereed):

[7] G.N. Arzhantseva, J. Díaz, J. Petit, J.D.P. Rolim, and M. Serna, Broadcasting on networks of sensors communicating through directional antennas,
Ambient Intelligence Computing, 1-12, Proceedings, CTI Press and Ellinika Grammata, 2003.   pdf

[6] G.N. Arzhantseva and J.D.P. Rolim, Considerations for a geometric model of the web,
Approximation and Randomization Algorithms in Communication Networks, Rome, 2002, 1-11, Proceedings, Carleton Scientific.

[5] G.N. Arzhantseva and J.D.P. Rolim, Computability and Complexity,
e-learning theoretical course of the Virtual Logic Laboratory (a project of the Swiss Virtual Campus), 90 pp. (electronic tutorial)

Short communications:

[4] G. Arzhantseva, A. Thom, A. Valette, Finite-dimensional approximations of discrete groups,,
Oberwolfach Rep., 8(2) (2011), 1429-1467.     pdf

[3] G. Arzhantseva, Uniform embeddings of groups into a Hilbert space,,
in I. Hambleton, E. Pedersen, A. Ranicki, H. Reich (eds.), Manifold perspectives, Oberwolfach Rep. 6(2) (2009), 1527-1529.     pdf

[2] G. Arzhantseva, The uniform Kazhdan property for SLn(Z), n>3,,
l'Enseignement Mathématique 54(2) (2008), 12.

[1] G. Arzhantseva, The entropy of a group endomorphismce,,
in G. Knieper, L. Polterovich, L. Potyagailo (eds.), Geometric group theory, hyperbolic dynamics and symplectic geometry, embeddings of groups into a Hilbert space, Oberwolfach Rep. 33 (2006), 2044-2045.     book

Lecture notes:

G.N. Arzhantseva and M. Lustig, A first course in geometric group theory, graduate textbook project.
G.N. Arzhantseva, Geometry of small cancellation and Burnside factors, lecture notes of the Borel seminar minicourse.
G.N. Arzhantseva, Infinite groups: Growth and Isoperimetry, lecture notes, the IIIe Cycle Romand de mathématiques.

Conference announcements:

G.N. Arzhantseva, Genericity of Howson's property of finitely presented groups,
International Algebraic Conference dedicated to the memory of D.K. Faddeev, Saint-Petersburg, Russia, 24-30 June, 1997. Abstracts, 158-159.

G.N. Arzhantseva, Generic classes of finitely presented groups,
International Algebraic Conference dedicated to the memory of D.K. Faddeev, Saint-Petersburg, Russia, 24-30 June, 1997. Abstracts, 158-159.

G.N. Arzhantseva, Generic classes of finitely presented groups,
International Conference "Mathematics. Modeling. Ecology" Volgograd, Russia, 27-31 May, 1996. Abstracts, p.23.