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arXiv:2312.14296 [math.GR]AbstractReferencesReviewsResources

Strong Property $(T)$ and relatively hyperbolic groups

Hermès Lajoinie-Dodel

Published 2023-12-21Version 1

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.

Comments: Comments are welcome!
Categories: math.GR, math.GT, math.MG
Subjects: 53C24, 20F65, 20F67, 19J35
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