Orbit equivalence rigidity and bounded cohomology

2006/11/01 by Nicolas Monod, Yehuda Shalom · 6 citations
Mathematics · #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology #Mathematics #Rigidity (electromagnetism) #Bounded function #Equivalence (formal languages) #Cohomology #Orbit (dynamics) #Pure mathematics #Mathematical analysis #Physics #Quantum mechanics

paper · pdf · doi:10.4007/annals.2006.164.825

openalex publication_date 2006/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

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.

Citations

• On Groups of Measure Preserving Transformations. I

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