Measure equivalence rigidity of the mapping class group

Abstract

We show that the mapping class group of a compact orientable surface with higher complexity has the following extreme 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 kernel. Moreover, we describe all lattice embeddings of the mapping class group into a locally compact second countable group. We also obtain similar results for finite direct products of mapping class groups.

39 pages

References in corpus (1)

• Orbit equivalence rigidity for ergodic actions of the mapping class group

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