Continuous orbit equivalence rigidity for left-right wreath product actions

Orbit Equivalence and Von Neumann Rigidity for Actions of Wreath Product Groups

of the Dissertation Orbit Equivalence and Von Neumann Rigidity for Actions of Wreath Product Groups

Orbit equivalence rigidity

Consider a countable group Γ acting ergodically by measure preserving transformations on a probability space (X,μ), and let RΓ be the corresponding orbit equivalence relation on X. The following rigidity phenomenon is shown: there exist group actions such that the equivalence relation RΓ on X determines the group Γ and the action (X,μ,Γ) uniquely, up to finite groups. The natural action of SLn(...

Orbit equivalence rigidity and bounded cohomology

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 factorizat...

Rigidity theorems for actions of product groups and countable Borel equivalence relations

Orbit Equivalence, Coinduced Actions and Free Products

The following result is proven. Let G 1 T 1 (X 1 , µ 1) and G 2 T 2 (X 2 , µ 2) be orbit-equivalent, essentially free, probability measure preserving actions of countable groups G 1 and G 2. Let H be any countable group. For i = 1, 2, let Γ i = G i * H be the free product. Then the actions of Γ 1 and Γ 2 coinduced from T 1 and T 2 are orbit-equivalent. As an application, it is shown that if Γ i...