Orbit equivalence rigidity and bounded cohomology

• 成果类型: Article
• 署名作者: Monod, Nicolas; Shalom, Yehuda
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.164.825
• 发表日期: 2006
• 页码: 825-878
• 关键词: locally compact-groups; word-hyperbolic groups; cocycle superrigidity; semisimple groups; SUBGROUPS; lattices; SPACES

摘要

We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative curvature geometry. Amongst our applications are (a) measurable Mostow-type rigidity theorems for products of negatively curved groups; (b) prime factorization results for measure equivalence; (c) superrigidity for orbit equivalence; (d) the first examples of continua of type II1 equivalence relations with trivial outer automorphism group that are mutually not stably isomorphic.