Measure equivalence rigidity of the mapping class group

Abstract

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.

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Authors

Yoshikata Kida

Max-Planck-Institut für Mathematik
Vivatsgasse 7
Bonn 53111
Germany
and
Department of Mathematics
Kyoto University
Kyoto 606-8502
Japan