Orbit equivalence rigidity and bounded cohomology
Group Theory
2007-05-23 v1
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.
Cite
@article{arxiv.math/0703165,
title = {Orbit equivalence rigidity and bounded cohomology},
author = {Nicolas Monod and Yehuda Shalom},
journal= {arXiv preprint arXiv:math/0703165},
year = {2007}
}
Comments
54 pages, published version