C¹ actions on manifolds by lattices in Lie groups

2018/01/11 by Aaron Brown, Brown, Aaron, Danijela Damjanović +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.1801.04009

openalex publication_date 2018/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study Zimmer's conjecture for C¹ actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds. We show that when the rank of an uniform lattice is larger than the dimension of the manifold, then the action factors through a finite group. For lattices in SL(n, \R), the dimensional bound is sharp.

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