Euclidean Artin–Tits groups are acylindrically hyperbolic

[摘要] 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.

[学科分类] 神经科学

[关键词] Euclidean Artin–Tits group;acylindrically hyperbolic;Garside group