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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… (More)

We present a short, self-contained, relatively simple proof to the growth di-chotomy of linear groups. The proof depends on the fixed point property of amenable groups, and the main tool is Furstenberg's Lemma regarding measures on projective spaces. ᮊ 1998 Academic Press Let G be a group generated by a finite subset S; define S n to be the set Ž. < n < of… (More)

6. Principal bundles, induction, and cohomology I. Principal bundles and induction of unitary representations II. A " transference " theorem III. The bundle-induction operation on the first cohomology 1. Introduction and discussion of the main results I. Introduction. Throughout the last two or three decades, the theory of rigidity, particularly in relation… (More)

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established in [MSb] hold for all… (More)

- YEHUDA SHALOM
- 1999

Let k be any locally compact non-discrete field. We show that finite invariant measures for k-algebraic actions are obtained only via actions of compact groups. This extends both Borel's density and fixed point theorems over local fields (for semisimple/solvable groups, resp.). We then prove that for k-algebraic actions, finitely additive finite invariant… (More)

- Yehuda Shalom
- Combinatorica
- 1997

- ALEX FURMAN, YEHUDA SHALOM
- 1998

Let µ be a probability measure on a locally compact group G, and suppose G acts measurably on a probability measure space (X, m), preserving the measure m. We study ergodic theoretic properties of the action along µ-i.i.d. random walks on G. It is shown that under a (necessary) spectral assumption on the µ-averaging operator on L 2 (X, m), almost surely the… (More)

- Pavel Bleher, Jens Bolte, +33 authors Audrey Terras

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