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1.a. Since its introduction by Kazhdan in [Ka], property (T ) became a fundamental concept in mathematics with a wide range of applications to such areas as: â€¢ The structure of infinite groupsâ€”finite generation and finite Abelianization of higher-rank lattices [Ka], obstruction to free or amalgamated splittings [Wa], [A], [M4], structure of normal subgroupsâ€¦ (More)

Let G be a group. It is obvious that if G has an infinite cyclic quotient, then G has a nontrivial action on the real line by orientation-preserving homeomorphisms. The converse is not true in general, but, using an idea of E.Ghys, we prove that the converse does hold for all finitely generated, amenable groups. The proof is surprisingly easy, and combinesâ€¦ (More)

We study geometric representations of GL(n, R) for a ring R. The structure of the associated Hecke algebras is analyzed and shown to be cellular. Multiplicities of the irreducible constituents of these representations are linked to the embedding problem of pairs of R-modules x âŠ‚ y.

- Uri Bader, Alex Furman
- 2010

We identify the images of the comparision maps from ordinary homology and Sobolev homology, respectively, to the `1-homology of a wordhyperbolic group with coefficients in complete normed modules. The underlying idea is that there is a subdivision procedure for singular chains in negatively curved spaces that is much more efficient (in terms of the `1-norm)â€¦ (More)

- Uri Bader, Alex Furman, Roman Sauer
- 2009

We study rigidity properties of lattices in Isom(H) SOn,1(R), n â‰¥ 3, and of surface groups in Isom(H2) SL2(R) in the context of integrable measure equivalence. The results for lattices in Isom(H), n â‰¥ 3, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification. Despite theâ€¦ (More)

- Uri Bader, Alex Furman, Roman Sauer
- 2013

An important application of the algebraic theory of L2-Betti numbers [10] (see Farber [8] for an alternative approach) is that the L2-Betti numbers Î² i (Î“ ) of a group Î“ vanish if it has a normal subgroup whose L2-Betti numbers vanish. With regard to the first L2-Betti number, one can significantly relax the normality condition to obtain similar vanishingâ€¦ (More)

- Uri Bader, Bruno Duchesne, Jean Lecureux
- 2016

We show that an amenable Invariant Random Subgroup of a locally compact second countable group lives in the amenable radical. This answers a question raised in the introduction of [AGV12]. We also consider an opposite direction, property (T), and prove a similar statement for this property. Yes, the IRS is amenable to working with you if you are cooperativeâ€¦ (More)

The main motivation of this paper arises from classical questions about actions of Lie groups preserving a geometric structure: which Lie groups can act on a manifold preserving a given structure, and which cannot? Which algebraic properties of the acting group have strong implications on the geometry of the manifold, such as local homogeneity, or on theâ€¦ (More)

We study a family of complex representations of the group GL n (o), where o is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL n (F) to its maximal compact subgroup GL n (o). We compute explicitly the transition matrix between a geometric basis of the Hecke algebraâ€¦ (More)

- Uri Bader, Wolfgang Bader
- Zeitschrift fur Laryngologie, Rhinologieâ€¦
- 1971