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arXiv · 2312.14296

Strong Property $(T)$ and relatively hyperbolic groups

Hermès Lajoinie-Dodel
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Abstract

We prove that relatively hyperbolic groups do not have Lafforgue strong Property $(T)$ with respect to Hilbert spaces. To do so we construct an unbounded affine representation of such groups, whose linear part is of polynomial growth of degree $2$. Moreover, this representation is proper for the metric of the coned-off graph.

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Hermès Lajoinie-Dodel. 2023-12-21. Strong Property $(T)$ and relatively hyperbolic groups. https://arxiv.org/abs/2312.14296

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