Regularity of conjugacies of algebraic actions of Zariski dense groups

Gorodnik, Alexander; Hitchman, Theron; Spatzier, Ralf

Regularity of conjugacies of algebraic actions of Zariski dense groups

Authors

Gorodnik, Alexander

Hitchman, Theron

Spatzier, Ralf

Description

Let α_0 be an affine action of a discrete group Γon a compact homogeneous space X and α_1 a smooth action of Γon X which is C^1-close to α_0. We show that under some conditions, every topological conjugacy between α_0 and α_1 is smooth. In particular, our results apply to Zariski dense subgroups of SL_d(Z) acting on the torus T^d and Zariski dense subgroups of a simple noncompact Lie group G acting on a compact homogeneous space X of G with an invariant measure.