Local rigidity of affine actions of higher rank groups and lattices

• 成果类型: Article
• 署名作者: Fisher, David; Margulis, Gregory
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.67
• 发表日期: 2009
• 页码: 67-122
• 关键词: partially hyperbolic actions; lie-groups; discrete subgroups; DYNAMICAL-SYSTEMS; normal forms; property t; compact; tori; foliations; MANIFOLDS

摘要

Let J be a semisimple Lie group with all simple factors of real rank at least two. Let Gamma < J be a lattice. We prove a very general local rigidity result about actions of J or Gamma. This shows that almost all so-called standard actions are locally rigid. As a special case, we see that any action of Gamma by toral automorphisms is locally rigid. More generally, given a manifold M on which Gamma acts isometrically and a torus T-n on which it acts by automorphisms, we show that the diagonal action on T-n x M is locally rigid. This paper is the culmination of a series of papers and depends heavily on our work in two recent articles. The reader willing to accept the main results of those papers as black boxes should be able to read the present paper without referring to them.