Measure equivalence rigidity and bi-exactness of groups |
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Authors: | Hiroki Sako |
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Institution: | Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan |
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Abstract: | We get three types of results on measurable group theory; direct product groups of Ozawa's class S groups, wreath product groups and amalgamated free products. We prove measure equivalence factorization results on direct product groups of Ozawa's class S groups. As consequences, Monod-Shalom type orbit equivalence rigidity theorems follow. We prove that if two wreath product groups A?G, B?Γ of non-amenable exact direct product groups G, Γ with amenable bases A, B are measure equivalent, then G and Γ are measure equivalent. We get Bass-Serre rigidity results on amalgamated free products of non-amenable exact direct product groups. |
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Keywords: | Measure equivalence Orbit equivalence rigidity Bi-exactness of groups |
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