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

Hermès Lajoinie-Dodel

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

Group Theory 2025-12-25 v1 Geometric Topology Metric Geometry

Authors: Hermès Lajoinie-Dodel

Abstract

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.

Keywords

hyperbolic groups hyperbolic geometry

Cite

@article{arxiv.2512.21169,
  title  = {Strong bolicity and the Baum-Connes conjecture for relatively hyperbolic groups},
  author = {Hermès Lajoinie-Dodel},
  journal= {arXiv preprint arXiv:2512.21169},
  year   = {2025}
}