Cocycle superrigidity for profinite actions of property (T) groups
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Publication:533849
DOI10.1215/00127094-2011-008zbMath1235.37005arXiv0805.2998OpenAlexW3105237982MaRDI QIDQ533849
Publication date: 10 May 2011
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0805.2998
ergodic actionorbit equivalenceergodic equivalence relationrelative property (T)profinite actioncocycle superrigidityorbit equivalent superrigid actionorbit equivalent superrigid group
General groups of measure-preserving transformations (28D15) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Classification of factors (46L36)
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Cites Work
- Unnamed Item
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- Some rigidity results for non-commutative Bernoulli shifts
- On property (T) for pairs of topological groups
- Amalgamated free products of weakly rigid factors and calculation of their symmetry groups
- Measure equivalence rigidity of the mapping class group
- On a class of II\(_1\) factors with at most one Cartan subalgebra
- Rigidity of commensurators and irreducible lattices
- Outer automorphism groups of some ergodic equivalence relations
- Fundamental groups for ergodic actions and actions with unit fundamental groups
- Superrigidity and countable Borel equivalence relations
- Gromov's measure equivalence and rigidity of higher rank lattices
- Orbit equivalence rigidity
- Cocycle and orbit equivalence superrigidity for malleable actions of \(w\)-rigid groups
- Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups
- Orbit equivalence rigidity and bounded cohomology
- Orbit equivalence rigidity for ergodic actions of the mapping class group
- Cocycle superrigidity and bounded cohomology for negatively curved spaces
- Strong rigidity of \(\text{II}_1\) factors arising from malleable actions of \(w\)-rigid groups. II
- On a class of type \(\text{II}_1\) factors with Betti numbers invariants
- Connection of the dual space of a group with the structure of its closed subgroups
- On rings of operators
- A survey of Measured Group Theory
- On the superrigidity of malleable actions with spectral gap
- On Groups of Measure Preserving Transformations. I
- Finitely-additive invariant measures on Euclidean spaces
- Kazhdan constants for SL (3, Z).
- On a class of II<sub xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> factors with at most one Cartan subalgebra, II
- Ergodic theory of amenable group actions. I: The Rohlin lemma
- An amenable equivalence relation is generated by a single transformation
- Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. II
- A converse to Dye’s theorem
- On Popa's Cocycle Superrigidity Theorem
