Euclidean Artin-Tits groups are acylindrically hyperbolic
Group Theory
2020-10-27 v1
Abstract
In this paper we show the statement in the title. To any Garside group of finite type, Wiest and the author associated a hyperbolic graph called the \emph{additional length graph} and they used it to show that central quotients of Artin-Tits groups of spherical type are acylindrically hyperbolic. In general, a euclidean Artin-Tits group is not \emph{a priori} a Garside group but McCammond and Sulway have shown that it embeds into an \emph{infinite-type} Garside group which they call a \emph{crystallographic Garside group}. We associate a \emph{hyperbolic} additional length graph to this crystallographic Garside group and we exhibit elements of the euclidean Artin-Tits group which act loxodromically and WPD on this hyperbolic graph.
Keywords
Cite
@article{arxiv.2010.13145,
title = {Euclidean Artin-Tits groups are acylindrically hyperbolic},
author = {Matthieu Calvez},
journal= {arXiv preprint arXiv:2010.13145},
year = {2020}
}