Euclidean Artin–Tits groups are acylindrically hyperbolic
Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 963-983
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In this paper, we prove that all Euclidean Artin–Tits groups are acylindrically hyperbolic. To any Garside group of finite type, Wiest and the author associated a hyperbolic graph called the 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 a priori a Garside group but McCammond and Sulway have shown that it embeds into an infinite-type Garside group which they call a crystallographic Garside group. We associate a hyperbolic additional length graph to this crystallographic Garside group and we exhibit elements of the Euclidean Artin–Tits group which act loxodromically and weakly properly discontinuously on this hyperbolic graph.
Classification :
20-XX
Mots-clés : Euclidean Artin–Tits group, acylindrically hyperbolic, Garside group
Mots-clés : Euclidean Artin–Tits group, acylindrically hyperbolic, Garside group
Affiliations des auteurs :
Matthieu Calvez 1
Matthieu Calvez. Euclidean Artin–Tits groups are acylindrically hyperbolic. Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 963-983. doi: 10.4171/ggd/683
@article{10_4171_ggd_683,
author = {Matthieu Calvez},
title = {Euclidean {Artin{\textendash}Tits} groups are acylindrically hyperbolic},
journal = {Groups, geometry, and dynamics},
pages = {963--983},
year = {2022},
volume = {16},
number = {3},
doi = {10.4171/ggd/683},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/683/}
}
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