Article
Acylindrical hyperbolicity and Artin-Tits groups of spherical type
Author/s | Calvez, Matthieu
Wiest, Bert |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2017 |
Deposit Date | 2017-07-06 |
Published in |
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Abstract | 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 ... 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 xG 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. |
Project ID. | 11140090
USA1555 PIA-CONICYT ACT1415 MTM2010-19355 |
Citation | Calvez, M. y Wiest, B. (2017). Acylindrical hyperbolicity and Artin-Tits groups of spherical type. Geometriae Dedicata, 1-17. |
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