Handbook of Teichm├╝ller Theory, Volume II

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pp: 297–367

DOI: 10.4171/055-1/10

Introduction to measurable rigidity of mapping class groups

Yoshikata Kida[1]

(1) The University of Tokyo, Japan

In this survey, we present an outline of the proof of measure equivalence and orbit equivalence rigidity results for mapping class groups. We also describe all locally compact second countable groups containing a lattice isomorphic to a mapping class group.

Keywords: Measure equivalence, measurable rigidity, orbit-equivalence, discrete measured groupoid, amenable action, reducible groupoids