In this paper we study a homological version of the asymptotic filling invariant divk defined by Brady and Farb in [BrFa] and show that it is a quasi-isometry invariant for all proper cocompact Hadamard spaces, i.e. proper cocompact CAT(0)-spaces, and that it can furthermore be used to detect the Euclidean rank of such spaces. We thereby extend results of [BrFa, Leu, Hin] from the setting of sy...

In this paper we show that many projective Anosov representations act convex cocompactly on some properly domain in real space. particular, if a non-elementary word hyperbolic group is not commensurable to non-trivial free product or the fundamental of closed surface, then any representation acts We also preserves domain, it (possibly different) domain. give three applications. First, into gene...

We give an upper bound for the number uΓ(n) of “overlattices” in the automorphism group of a tree, containing a fixed lattice Γ with index n. For an example of Γ in the automorphism group of a 2p-regular tree whose quotient is a loop, we obtain a lower bound of the asymptotic behavior as well. Nous donnons une borne supérieure pour le nombre uΓ(n) de “surréseaux” contenant un réseau fixé d’indi...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

In this paper, we construct for the first time, Witten genus and elliptic genera on noncompact manifolds with a proper cocompact action by an almost connected Lie group prove vanishing rigidity results that generalise known compact actions manifolds. We also compute our some interesting examples, study non-spinc case in appendix.

We explain simple methods to establish the property of Rapid Decay for a number of groups arising geometrically. Those lead to new examples of groups with the property of Rapid Decay, notably including non-cocompact lattices in rank one Lie groups.

We show that, under some very weak assumption of effective variation for the magnetic field, a periodic Schrödinger operator with magnetic wells on a noncompact Riemannian manifold M such that H(M, R) = 0 equipped with a properly disconnected, cocompact action of a finitely generated, discrete group of isometries has an arbitrarily large number of spectral gaps in the semi-classical limit.