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(...
متن کاملOrbit 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...
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 ...
متن کاملOrbit 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
متن کاملGraph Algebras and Orbit Equivalence
We introduce the notion of orbit equivalence of directed graphs, following Matsumoto’s notion of continuous orbit equivalence for topological Markov shifts. We show that two graphs in which every cycle has an exit are orbit equivalent if and only if there is a diagonal-preserving isomorphism between their C∗-algebras. We show that it is necessary to assume that every cycle has an exit for the f...
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ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 1999
ISSN: 0003-486X
DOI: 10.2307/121063