Indira Chatterji

FROM WALL SPACES TO CAT(0) CUBE COMPLEXES

We explain how to adapt a construction due to M. Sageev in order to construct a proper action of a group on a CAT(0) cube complex starting from a proper action of the group on a wall space.

Connected Lie groups and property RD

For a locally compact group, property RD gives a control on the convolution norm of any compactly supported measure in terms of the

Property (RD) for Cocompact Lattices in a Finite Product of Rank One Lie Groups with Some Rank Two Lie Groups

L^2

The median class and superrigidity of actions on CAT(0) cube complexes

-norm of its density and the diameter of its support. We give a complete classification of those Lie groups with property RD.

Homotopy idempotents on manifolds and Bass' conjectures

We apply V. Lafforgue′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.

Cryptosystems using subgroup distortion

We define a bounded cohomology class, called the {\em median class}, in the second bounded cohomology -- with appropriate coefficients --of the automorphism group of a finite dimensional CAT(0) cube complex X. The median class of X behaves naturally with respect to taking products and appropriate subcomplexes and defines in turn the {\em median class of an action} by automorphisms of X. We show that the median class of a non-elementary action by automorphisms does not vanish and we show to which extent it does vanish if the action is elementary. We obtain as a corollary a superrigidity result and show for example that any irreducible lattice in the product of at least two locally compact connected groups acts on a finite dimensional CAT(0) cube complex X with a finite orbit in the Roller compactification of X. In the case of a product of Lie groups, the Appendix by Caprace allows us to deduce that the fixed point is in fact inside the complex X. In the course of the proof we construct a \Gamma-equivariant measurable map from a Poisson boundary of \Gamma with values in the non-terminating ultrafilters on the Roller boundary of X.

NEW EXAMPLES OF FINITELY PRESENTED GROUPS WITH STRONG FIXED POINT PROPERTIES

The Bass trace conjectures are placed in the setting of homotopy idempotent selfmaps of manifolds. For the strong conjecture, this is achieved via a formulation of Geoghegan. The weaker form of the conjecture is reformulated as a comparison of ordinary and L^2-Lefschetz numbers.

Geometric and Cohomological Methods in Group Theory: Hattori-Stallings trace and Euler characteristics for groups

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

Kazhdan and Haagerup properties from the median viewpoint

The aim of this note is to give an easy example of a finitely presented group that cannot act without a fix point on a CAT(0) space of finite dimension. Such an example has been recently constructed by Arjantseva et al., using other techniques

SOME GEOMETRIC GROUPS WITH RAPID DECAY

We discuss properties of the complete Euler characteristic of a group G of type FP over the complex numbers and we relate it to the L2-Euler characteristic of the centralizers of the elements of G.