Monod, Nicolas; Shalom, Yehuda Orbit equivalence rigidity and bounded cohomology. (English) Zbl 1129.37003 Ann. Math. (2) 164, No. 3, 825-878 (2006). Summary: We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative curvature geometry. Amongst our applications are (a) measurable Mostow-type rigidity theorems for products of negatively curved groups; (b) prime factorization results for measure equivalence; (c) superrigidity for orbit equivalence; (d) the first examples of continua of type II\(_1\) equivalence relations with trivial outer automorphism group that are mutually not stably isomorphic. Cited in 3 ReviewsCited in 82 Documents MSC: 37A20 Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations 22F10 Measurable group actions 37A15 General groups of measure-preserving transformations and dynamical systems Keywords:rigidity theorems; negatively curved groups; prime factorization results; superrigidity; equivalence relations PDFBibTeX XMLCite \textit{N. Monod} and \textit{Y. Shalom}, Ann. Math. (2) 164, No. 3, 825--878 (2006; Zbl 1129.37003) Full Text: DOI arXiv Euclid