Gaboriau, Damien 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 C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 5, 365-370 (2000). 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. Cited in 3 Documents MSC: 37A15 General groups of measure-preserving transformations and dynamical systems 22F10 Measurable group actions Keywords:countable discrete groups; rigidity results PDFBibTeX XMLCite \textit{D. Gaboriau}, C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 5, 365--370 (2000; Zbl 0988.37003) Full Text: DOI