Acylindrical hyperbolicity and Artin-Tits groups of spherical type

作者：Calvez Matthieu^*; Wiest Bert

来源：Geometriae Dedicata, 2017, 191(1): 199-215.

DOI：10.1007/s10711-017-0252-y

• Acylindrically hyperbolic
• Artin-Tits groups

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 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.

• 出版日期2017-12