Measure equivalence rigidity of the mapping class group

• 成果类型: Article
• 署名作者: Kida, Yoshikata
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 1851-1901
• 关键词: bounded cohomology; malleable actions; AUTOMORPHISMS; complexes; CURVES; superrigidity; SUBGROUPS

摘要

We show that the mapping class group of a compact orientable surface with higher complexity satisfies the following rigidity in the sense of measure equivalence: If the mapping class group is measure equivalent to a discrete group, then they are commensurable up to finite kernels. Moreover, we describe all locally compact second countable groups containing a lattice isomorphic to the mapping class group. We obtain similar results for finite direct products of mapping class groups.