We explain how to adapt a construction of M. Sageevâ€™s to construct a proper action on a CAT(0) cube complex starting from a proper action on a wall space.

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, notablyâ€¦ (More)

We prove that the Bost Conjecture on the `-assembly map for countable discrete groups implies the Bass Conjecture. It follows that all amenable groups satisfy the Bass Conjecture.

For a locally compact group, the property of rapid decay (property RD) gives a control on the convolutor norm of any compactly supported function in terms of its L2-norm and the diameter of itsâ€¦ (More)

We prove the existence of a close connection between spaces with measured walls and median metric spaces. We then relate properties (T) and Haagerup (a-T-menability) to actions on median spaces andâ€¦ (More)

We apply V. Lafforgueâ€™s techniques to establish property (RD) for cocompact lattices in a finite product of rank one Lie groups with Lie groups whose restricted root system is of type A2. We recallâ€¦ (More)

A geodesic metric space is Î´-hyperbolic in the sense of Gromov if and only if the intersection of any two metric balls is almost a ball. In particular, R-trees can be characterised by the propertyâ€¦ (More)

We define a transfer map in the setting of bounded cohomology with certain metric G-module coefficients. As an application, we extend a theorem on the comparison map from Borelbounded to Borelâ€¦ (More)

In this paper we propose cryptosystems based on subgroup distortion in hyperbolic groups. We also include concrete examples of hyperbolic groups as possible platforms.