Sofic equivalence relations. (English) Zbl 1417.37046
Summary: We introduce the notion of sofic measurable equivalence relations. Using them we prove that Connes’ Embedding Conjecture as well as the Measurable Determinant Conjecture of W. Lück et al. [J. Topol. Anal. 2, No. 2, 145–171 (2010; Zbl 1195.57053)] hold for treeable equivalence relations.
MSC:
| 37A20 | Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations |
| 20F65 | Geometric group theory |
| 03E15 | Descriptive set theory |
| 46L10 | General theory of von Neumann algebras |
Keywords:
measurable equivalence relations; Connes embedding conjecture; sofic groups; von Neumann algebrasCitations:
Zbl 1195.57053References:
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