An uncountable family of nonorbit equivalent actions of 𝔽_{𝕟}

DOI10.1090/S0894-0347-05-00480-7zbMath1155.37302arXivmath/0306011MaRDI QIDQ4679397

Damien Gaboriau, Sorin Popa

Publication date: 30 May 2005

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0306011

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Dynamical systems and the theory of (C^*)-algebras (37A55)

Related Items (27)

On II\(_{1}\) factors arising from 2-cocycles of \(w\)-rigid groups ⋮ A unique decomposition result for HT factors with torsion free core ⋮ Rigidity for equivalence relations on homogeneous spaces ⋮ Some unique group-measure space decomposition results ⋮ Relative property (T) and linear groups. ⋮ Free product actions with relative property (T) and trivial outer automorphism groups ⋮ Stable orbit equivalence of Bernoulli actions of free groups and isomorphism of some of their factor actions ⋮ Families of hyperfinite subfactors with the same standard invariant and prescribed fundamental group ⋮ Rigidity for group actions on homogeneous spaces by affine transformations ⋮ Incomparable actions of free groups ⋮ Orbit inequivalent actions for groups containing a copy of \(\mathbb{F}_{2}\) ⋮ Cocycle superrigidity for profinite actions of irreducible lattices ⋮ Amalgamated free products of weakly rigid factors and calculation of their symmetry groups ⋮ Topological properties of full groups ⋮ Orbit equivalence and Borel reducibility rigidity for profinite actions with spectral gap ⋮ Approximate equivalence of group actions ⋮ Actions of $\mathbb {F}_\infty $ whose II$_1$ factors and orbit equivalence relations have prescribed fundamental group ⋮ Relative property (T) for the subequivalence relations induced by the action of SL\(_2(\mathbb Z)\) on \(\mathbb T^2\) ⋮ Modular actions and amenable representations ⋮ Strong rigidity of \(\text{II}_1\) factors arising from malleable actions of \(w\)-rigid groups. I ⋮ On a class of II\(_1\) factors with at most one Cartan subalgebra ⋮ On the superrigidity of malleable actions with spectral gap ⋮ Group amenability and actions on \(\mathcal{Z} \)-stable C*-algebras ⋮ Entropy, Shannon orbit equivalence, and sparse connectivity ⋮ Weak density of orbit equivalence classes of free group actions ⋮ All properly ergodic Markov chains over a free group are orbit equivalent ⋮ Subequivalence relations and positive-definite functions

Cites Work

• Property T and asymptotically invariant sequences
• Hyperfinite and \(II_ 1 \)actions for nonamenable groups
• An example of a non nuclear C*-algebra, which has the metric approximation property
• Fundamental groups for ergodic actions and actions with unit fundamental groups
• \(\ell^2\) invariants of equivalence relations and groups
• Cost of equivalence relations and groups
• A lemma for cost attained
• Orbit equivalence rigidity and bounded cohomology
• On a class of type \(\text{II}_1\) factors with Betti numbers invariants
• Uncountably many \(II_1\) factors
• On rings of operators
• On rings of operators. IV
• On Groups of Measure Preserving Transformations. I
• Finitely-additive invariant measures on Euclidean spaces
• Property T for von Neumann Algebras
• Kazhdan constants for SL (3, Z).
• Ergodic theory of amenable group actions. I: The Rohlin lemma
• An amenable equivalence relation is generated by a single transformation
• A converse to Dye’s theorem
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: An uncountable family of nonorbit equivalent actions of 𝔽_{𝕟}