Hermès Lajoinie-Dodel

arXiv2025

Strong bolicity and the Baum-Connes conjecture for relatively hyperbolic groups

We construct a strongly bolic metric for a certain class of relatively hyperbolic groups, which includes those with CAT(0) parabolics and virtually abelian parabolics. If we further assume that the parabolics satisfy (RD), applying a theorem of Lafforgue, we deduce the Baum-Connes conjecture for these groups. One of the key ingredients in our construction is the use of random coset representatives called masks, developed by Chatterji and Dahmani.

math.GR↗

arXiv2023

Strong Property $(T)$ and relatively hyperbolic groups

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.

math.GR↗