Integrable measure equivalence and rigidity of hyperbolic lattices

• 成果类型: Article
• 署名作者: Bader, Uri; Furman, Alex; Sauer, Roman
• 署名单位: Technion Israel Institute of Technology; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Chicago
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0445-9
• 发表日期: 2013
• 页码: 313-379
• 关键词: amalgamated free-products; mapping class group; bounded cohomology; malleable actions; ii1 factors; cocycle superrigidity; convergence groups; singular homology; ergodic actions; INVARIANTS

摘要

We study rigidity properties of lattices in , na parts per thousand yen3, and of surface groups in in the context of integrable measure equivalence. The results for lattices in , na parts per thousand yen3, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification. Despite the lack of Mostow rigidity for n=2 we show that cocompact lattices in allow a similar integrable measure equivalence classification.