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On \(L^2\)-(co-)homology of measure-preserving actions. (Sur la (co-)homologie \(L^2\) des actions préservant une mesure.) (French. Abridged English version) Zbl 0988.37003

Summary: We show that \(\ell^2\)-Betti numbers for countable discrete groups are orbit equivalence invariants. This gives new rigidity results. We obtain a generalization of a result by W. Lück and applications to treeability of groups.

MSC:

37A15 General groups of measure-preserving transformations and dynamical systems
22F10 Measurable group actions
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