Gromov's measure equivalence and rigidity of higher rank lattices

• 成果类型: Article
• 署名作者: Furman, A
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121062
• 发表日期: 1999
• 页码: 1059-1081
• 关键词: semisimple lie-groups; symmetrical spaces

摘要

In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the motivations for this notion. The main result of this paper is ME rigidity of higher rank lattices: any countable group which is ME to a lattice in a simple Lie group G of higher rank, is commensurable to a lattice in G.