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