Orbit equivalence rigidity and bounded cohomology

Nicolas Monod; Yehuda Shalom

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arXiv · math/0703165

Orbit equivalence rigidity and bounded cohomology

Nicolas Monod·Yehuda Shalom

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Abstract

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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Nicolas Monod, Yehuda Shalom. 2007-03-06. Orbit equivalence rigidity and bounded cohomology. https://arxiv.org/abs/math/0703165

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