Danijela Damjanovic, Anatole Katok
Periodic Cycle Functionals and Cocycle Rigidity for Certain Partially Hyperbolic R$^k$ Actions
Preprint series: ESI preprints

MSC:

22E99 None of the above but in this section

58F99 None of the above but in this section

Abstract: We give a proof of cocycle rigidity in H\"older and smooth categories for Cartan actions on $\slnr/\Gamma$ and $\slnc/\Gamma$ for $n\ge 3$ and $\Gamma$ cocompact lattice, and for restrictions of those actions to subspaces which contain a
two-dimensional plane in a general position. This proof does not use harmonic analysis, it relies completely on the structure of stable and unstable foliations of the action. The key new ingredient is the use of the description of relations in the group $SL_n$.

Keywords: cocycles, rigidity, group actions, weyl chamber flow