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- W2950402743 abstract "Let $Aneq A_1, A_2, I_{2m}$ be an irreducible Artin--Tits group of spherical type. We show that periodic elements of $A$ and the elements preserving some parabolic subgroup of $A$ act elliptically on the additional length graph $mathcal{C}_{AL}(A)$, an 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 $gin A$ such that $langle P,g ranglecong P* langle g rangle$ 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 ${omega(A_n,mathcal{S})}_{nin mathbb{N}}$ of exponential growth rates of braid groups with respect to the Garside generating set, goes to infinity." @default.
- W2950402743 created "2019-06-27" @default.
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- W2950402743 date "2019-06-14" @default.
- W2950402743 modified "2023-09-30" @default.
- W2950402743 title "Parabolic subgroups acting on the additional length graph" @default.
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