منابع مشابه
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(...
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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...
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Let X and Y be Polish spaces with non-atomic Borel measures μ and ν of full support. Suppose that T and S are ergodic non-singular homeomorphisms of (X, μ) and (Y, ν) with continuous Radon-Nikodym derivatives. Suppose that either they are both of type III1 or that they are both of type IIIλ, 0 < λ < 1 and, in the IIIλ case, suppose in addition that both ‘topological asymptotic ranges’ (defined ...
متن کاملOrbit equivalence, flow equivalence and ordered cohomology
We study self-homeomorphisms of zero dimensional metrizable compact Hausdorff spaces by means of the ordered first cohomology group, particularly in the light of the recent work of Giordano, Putnam, and Skau on minimal homeomorphisms. We show that flow equivalence of systems is analogous to Morita equivalence between algebras, and this is reflected in the ordered cohomology group. We show that ...
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of the Dissertation Orbit Equivalence and Von Neumann Rigidity for Actions of Wreath Product Groups
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2016
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2016.98