Acylindrical hyperbolicity and Artin-Tits groups of spherical type - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Geometriae Dedicata Année : 2017

Acylindrical hyperbolicity and Artin-Tits groups of spherical type

Résumé

We prove that, for any irreducible Artin-Tits group of spherical type $G$, the quotient of $G$ by its center is acylindrically hyperbolic. This is achieved by studying the additional length graph associated to the classical Garside structure on $G$, and constructing a specific element $x_G$ of $G/Z(G)$ whose action on the graph is loxodromic and WPD in the sense of Bestvina-Fujiwara; following Osin, this implies acylindrical hyperbolicity. Finally, we prove that "generic" elements of $G$ act loxodromically, where the word "generic" can be understood in either of the two common usages: as a result of a long random walk or as a random element in a large ball in the Cayley graph.

Dates et versions

hal-01338184 , version 1 (28-06-2016)

Identifiants

Citer

Matthieu Calvez, Bert Wiest. Acylindrical hyperbolicity and Artin-Tits groups of spherical type. Geometriae Dedicata, 2017, 191 (1), pp.199-215. ⟨10.1007/s10711-017-0252-y⟩. ⟨hal-01338184⟩
182 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More