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Antolín Pichel, Yago and Cumplido, María
(2021)
*Parabolic subgroups acting on the additional length graph.*
Algebraic & Geometric Topology, 21
(4).
pp. 1791-1816.
ISSN 1472-2747

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Official URL: https://doi.org/10.2140/agt.2021.21.1791

## Abstract

Let A ≠ A1;A2;I2m be an irreducible Artin–Tits group of spherical type. We show that the periodic elements of A and the elements preserving some parabolic subgroup of A act elliptically on the additional length graph CAL(A), a hyperbolic, infinite diameter graph associated to A constructed by Calvez and Wiest to show that A/Z(A) is acylindrically hyperbolic. We use these results to find an element g ∈ A such that <P,g> ≅ P * <g> for every proper standard parabolic subgroup P of A. The length of g is uniformly bounded with respect to the Garside generators, independently of A. This allows us to show that, in contrast with the Artin generators case, the sequence ω(An,S)(with n ∈ N) of exponential growth rates of braid groups, with respect to the Garside generating set, goes to infinity.

Item Type: | Article |
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Uncontrolled Keywords: | Braid groups; Artin groups; Geometric group theory |

Subjects: | Sciences > Mathematics > Algebra Sciences > Mathematics > Group Theory |

ID Code: | 69511 |

Deposited On: | 26 Jan 2022 16:48 |

Last Modified: | 10 Feb 2022 16:51 |

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