Orbit equivalence rigidity and bounded cohomology

Nicolas Monod*, Yehuda Shalom

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 II1 equivalence relations with trivial outer automorphism group that are mutually not stably isomorphic.

Original languageEnglish
Pages (from-to)825-878
Number of pages54
JournalAnnals of Mathematics
Issue number3
StatePublished - Nov 2006


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