English

XXL type Artin groups are CAT(0) and acylindrically hyperbolic

Metric Geometry 2021-01-27 v4 Geometric Topology

Abstract

We describe a simple locally CAT(0) classifying space for extra extra large type Artin groups (with all labels at least 5). Furthermore, when the Artin group is not dihedral, we describe a rank 1 periodic geodesic, thus proving that extra large type Artin groups are acylindrically hyperbolic. Together with Property RD proved by Ciabonu, Holt and Rees, the CAT(0) property implies the Baum-Connes conjecture for all XXL type Artin groups.

Keywords

Cite

@article{arxiv.1905.11032,
  title  = {XXL type Artin groups are CAT(0) and acylindrically hyperbolic},
  author = {Thomas Haettel},
  journal= {arXiv preprint arXiv:1905.11032},
  year   = {2021}
}

Comments

12 pages, 5 figures. To appear in Annales de l'Institut Fourier