"Geometry and Analysis on Groups" Research Seminar
Uniform lattices acting on RAAG complexes.
Jingyin Huang (Ohio State University)
A classical result by Bieberbach says that uniform lattices acting on
Euclidean spaces by isometries are virtually free abelian. On the
other hand, uniform lattices acting on trees are virtually free. This
motivates the study of commensurability classification of uniform
lattices acting on CAT (0) cube complexes associated with right-angled
Artin groups (RAAG complexes). These complexes can be thought as
"interpolations" between Euclidean spaces and trees. Uniform lattices acting on the same RAAG complex may not belong to the same commensurability class, as there are irreducible lattices acting on products of trees. However, we show that the tree times tree obstruction is the only obstruction for commensurability of label-preserving lattices acting on RAAG complexes.