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

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

2009-12-06

arxiv.org/abs/0912.1091v1

Mathematics

Group Theory

Accepted to Bulletin of the Belgian Mathematical Society

Scientific paper

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 $\R$ is any countable unital ring of characteristic 0.

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