A converse to Dye's theorem

By Greg Hjorth. 2004

85 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e8ff40013782db91bd1884523a4d9f51c9e8aff5

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In Algebra and Number Theory

In Atomic and Molecular Physics, and Optics

In Mathematical Physics

Citations in the corpus

On Popa's Cocycle Superrigidity Theorem (2006, background): “Here we shall the proof for the special case of discrete target group, following Hjorth’s [14].”
A SURVEY OF MEASURED GROUP THEORY (2009, unknown): “Property (T): Γ has property (T) (Kazhdan [68]) if for every unitary Γ-representation π: 1Γ ≺ π implies 1Γ < π.”
AMENABLE ACTIONS AND ALMOST INVARIANT SETS (2007, background): “show that the action of Γ on X is amenable iff the shift Γ MX has almost invariant sets.”
Property (T) and rigidity for actions on Banach spaces (2005, methodology): “ fundamental group is countable [C] or even trivial [Po1]); rigidity theorems for the factors associated to Kazhdan group [Po2]; • Ergodic theory – rigidity results related to Orbit Equivalence [Po3],[Hj]; the Banach–Ruziewicz problem [M3],[Su]; • Smooth dynamics–local rigidity [FM1],[FM2]; actions ”
Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups (2006, background): “The inner automorphism group InnR, also called full group ofR, consists of ∆ ∈ Aut(X,µ) such that (x,∆(x)) ∈ R for almost all x ∈ X .”
Orbit inequivalent actions for groups containing a copy of $\mathbb{F}_{2}$ (2006, background): “For a non-amenable group , it is known that admits at least two non-OE actions [5, 18, 36].”
Borel Equivalence Relations (2010, background): “Moreoever the discussion of Borel equivalence relations is organized around the Borel reducibility order, ≤B, rather than notions such as orbit equivalence, as found in say [20], [18], [21], [53], [28], or notions of isomorphism, as discussed in [9].”
Integrable measure equivalence and rigidity of hyperbolic lattices (2010, background): “The study of measure equivalence and related problems has recently experienced a rapid growth, with [14, 15, 21, 22, 26, 28, 29, 33, 35, 43, 46–49, 51] being only a partial list of important advances.”
On the superrigidity of malleable actions with spectral gap (2006, background): “bras ([C3,4]) and by Zimmer in OE ergodic theory ([Z1,2]). This changed dramatically over the last 7-8 years, with the advent of a variety of striking rigidity results ([Fu1], [G1,2], [MoSh], [P1-8], [H], [HK], [Ki]; see [P9] for a survey; also [Sh] for a survey on OE rigidity). Our aim in this pape”
Rigidity results for Bernoulli actions and their von Neumann algebras (after Sorin Popa) (2006, background): “of mutually non orbit equivalent actions. The existence of a continuum of non orbit equivalent actions of an inﬁnite property (T) group had been established before in a non-constructive way by Hjorth [27], who exhibits a continuous family of actions such that every action in the family is orbit equi”
Cocycle Superrigidity for Profinite Actions of Property (T) Groups (2008, unknown): “Γ →U(L2(R,µ˜)) be the unitary representation deﬁned by π t,t′(γ)(f)(x,y) = f(α t(γ−1)(x),α t′(γ−1)(y)), 26 ADRIAN IOANA for all γ∈Γ,f∈L2(R,µ˜),(x,y) ∈R. Using the property (T) of Γ as in Section 2 of [Hj], we can ﬁnd t,t′ ∈S∩(3/4,1) such that t<t′ and π t,t′ admits an invariant vector f∈L2(R,µ˜) ”