李群中格对流形的$C^1$作用
$C^1$ actions on manifolds by lattices in Lie groups
摘要：
本文研究了紧致流形上有限中心的高秩单李群的格子群的$C^1$作用的Zimmer猜想。证明了当一致格的秩大于流形的维数时，作用因子通过有限群。对于$SL(n, \R)$中的晶格，维数边界是尖锐的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
