Vanishing of the reduced $\ell_p$-cohomology of groups with infinite center

Piotr W. Nowak
Thursday, July 25, 2013 - from 16:30 to 16:55
We consider the representation of a group on its reduced $\ell_p$-cohomology and use it to show that the reduced $\ell_p$-cohomology with coefficients in bounded Banach modules vanishes for groups with infinite center, in degree 1. This generalizes and gives a new proof of a theorem, which in various weaker versions was proved earlier by Gromov, and Martin and Valette. We also show that our result implies the vanishing of the reduced cohomology of the group, with coefficients in a large class of bounded reflexive Banach modules.