Abstract
We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping class group for a compact orientable surface with higher complexity. We prove similar rigidity results for a finite direct product of mapping class groups as well.
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Kida, Y. Orbit equivalence rigidity for ergodic actions of the mapping class group. Geom Dedicata 131, 99–109 (2008). https://doi.org/10.1007/s10711-007-9219-8
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DOI: https://doi.org/10.1007/s10711-007-9219-8