Orbit equivalence rigidity and bounded cohomology

Details Orbit equivalence rigidity and bounded cohomology Orbit equivalence rigidity and bounded cohomology

2007-03-06

arxiv.org/abs/math/0703165v1

Ann. of Math. (2) 164 (2006), no. 3, 825--878

Mathematics

Group Theory

54 pages, published version

Scientific paper

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.

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