C1 actions on manifolds by lattices in Lie groups

In this paper we study Zimmer's conjecture for C-1 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.

Automated summary

This paper studies Zimmer's conjecture for C-1 actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds. It is shown that when the rank of a uniform lattice is larger than the dimension of the manifold, the action factors through a finite group. The dimensional bound is sharp for lattices in SL(n, R).