English

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 (T)(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 22. 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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R2 v1 2026-06-28T13:59:18.533Z