Name: Strong property (T) and relatively hyperbolic groups
Creator: Lajoinie-Dodel, Hermès
Keywords: relatively hyperbolic groups, Rigidity results, Geometric Topology (math.GT), Metric Geometry (math.MG), Group Theory (math.GR), Hyperbolic groups and nonpositively curved groups, strong property $(T)$, 53C24, 20F65, 20F67, 19J35, Obstructions to group actions ($K$-theoretic aspects), Mathematics - Geometric Topology

Strong property $(T)$ and relatively hyperbolic groups

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 25 Apr 2025Embargo end date: 01 Jan 2023 English Publisher:Springer Science and Business Media LLCJournal:Mathematische Zeitschrift, volume 310 (issn: 0025-5874, eissn: 1432-1823,

Authors: Lajoinie-Dodel, Hermès;

doi: 10.1007/s00209-025-03742-6 , 10.48550/arxiv.2312.14296

arXiv: http://arxiv.org/abs/2312.14296

Strong property (T) and relatively hyperbolic groups

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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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Keywords

relatively hyperbolic groups, Rigidity results, Geometric Topology (math.GT), Metric Geometry (math.MG), Group Theory (math.GR), Hyperbolic groups and nonpositively curved groups, strong property $(T)$, 53C24, 20F65, 20F67, 19J35, Obstructions to group actions ($K$-theoretic aspects), Mathematics - Geometric Topology, Gromov hyperbolicity, rigidity, Mathematics - Metric Geometry, FOS: Mathematics, Geometric group theory, Mathematics - Group Theory

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