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Parabolic subgroups
acting on the additional length graph
Yago Antolín and María Cumplido |
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Algebraic & Geometric Topology 21 (2021) 1791–1816
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Abstract |
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Let be an irreducible Artin–Tits group of spherical type. We show that the periodic elements of and the elements preserving some parabolic subgroup of act elliptically on the additional length graph , a hyperbolic, infinite diameter graph associated to constructed by Calvez and Wiest to show that is acylindrically hyperbolic. We use these results to find an element such that for every proper standard parabolic subgroup of . The length of is uniformly bounded with respect to the Garside generators, independently of . This allows us to show that, in contrast with the Artin generators case, the sequence of exponential growth rates of braid groups, with respect to the Garside generating set, goes to infinity. |
Keywords
braid groups, Artin groups, Garside groups, parabolic
subgroups, acylindrically hyperbolic groups, growth of
groups, relative growth
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Mathematical Subject Classification 2010
Primary: 20F36, 20F65
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References |
Publication
Received: 23 September 2019
Revised: 10 July 2020
Accepted: 30 July 2020
Published: 18 August 2021
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Authors |
| Yago Antolín | |
| Departamento de Matemáticas Universidad Autónoma de Madrid Instituto de Ciencias Matemáticas Madrid Spain |
Algebra Geometría y Topología Universidad Complutense de Madrid Madrid Spain |
| María Cumplido | |
| IMB, UMR 5584, CNRS Université Bourgogne Franche-Comté Dijon France |
Departamento de Álgebra Universidad de Sevilla Sevilla Spain |
