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arXiv · 0803.4129

Regularity of conjugacies of algebraic actions of Zariski dense groups

Alexander Gorodnik·Theron Hitchman·Ralf Spatzier
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Abstract

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.

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Alexander Gorodnik, Theron Hitchman, Ralf Spatzier. 2008-06-08. Regularity of conjugacies of algebraic actions of Zariski dense groups. https://arxiv.org/abs/0803.4129

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