Strong Property $(T)$ and relatively hyperbolic groups
Group Theory
2023-12-25 v1 Geometric Topology
Metric Geometry
Abstract
We prove that relatively hyperbolic groups do not have Lafforgue strong Property 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 . Moreover, this representation is proper for the metric of the coned-off graph.
Keywords
Cite
@article{arxiv.2312.14296,
title = {Strong Property $(T)$ and relatively hyperbolic groups},
author = {Hermès Lajoinie-Dodel},
journal= {arXiv preprint arXiv:2312.14296},
year = {2023}
}
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