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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: • The structure of infinite groups—finite generation and finite Abelianization of higher-rank lattices [Ka], obstruction to free or amalgamated splittings [Wa], [A], [M4], structure of normal subgroups(More)
We study rigidity properties of lattices in Isom(H) SOn,1(R), n ≥ 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 ≥ 3, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification. Despite the(More)
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 β i (Γ ) of a group Γ 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 vanishing(More)
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 cooperative(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 algebra(More)