Zagliki稠密群代数作用共轭的正则性
Regularity of conjugacies of algebraic actions of Zariski dense groups
摘要：
设α_0是离散群Γ在紧齐性空间X上的仿射作用，α_1是Γ在X上的光滑作用，它是C^1-接近α_0的.证明了在一定条件下，α_0和α_1之间的拓扑共轭都是光滑的.特别地，我们的结果适用于SL_d（Z）作用在环面T^d上的Zerkiki稠密子群和作用在G的具有不变测度的紧齐性空间X上的单非紧李群G的Zerkiki稠密子群.
英文摘要：
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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