Measure Equivalence Rigidity and Bi-exactness of Groups

Details Measure Equivalence Rigidity and Bi-exactness of Groups Measure Equivalence Rigidity and Bi-exactness of Groups

2009-01-21

arxiv.org/abs/0901.3376v5

J. Funct. Anal. 257 (2009), no. 10, 3167-3202

Mathematics

Group Theory

34 pages

Scientific paper

10.1016/j.jfa.2009.04.012

We get three types of results on measure equivalence rigidity; direct product groups of Ozawa's class $\mathcal{S}$ groups, wreath product groups and amalgamated free products. We prove measure equivalence factorization results on direct product groups of Ozawa's class $\mathcal{S}$ groups. As consequences, Monod--Shalom type orbit equivalence rigidity theorems follow. We prove that if two wreath product groups $A \wr G$, $B \wr \Gamma$ of non-amenable exact direct product groups $G$, $\Gamma$ with amenable bases $A$, $B$ are measure equivalent, then $G$ and $\Gamma$ are measure equivalent. We get Bass--Serre rigidity results on amalgamated free products of non-amenable exact direct product groups.

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