Relative Property (T) and the Vanishing of the first ${\ell }^2$-Betti number

Abstract

In this paper, we show that certain families with relative property (T) have trivial first ${\ell }^2$-Betti number. We apply this to the elementary matrix group $\EL_n(\R)$ where $\mathbb{R}$ is any countable unital ring of characteristic 0.

Accepted to Bulletin of the Belgian Mathematical Society

References in corpus (1)

• Group cocycles and the ring of affiliated operators