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Pré-Publication, Document De Travail Année : 2021

Morse elements in Garside groups are strongly contracting

Résumé

We prove that in the Cayley graph of any braid group modulo its center $B_n/Z(B_n)$, equipped with Garside's generating set, the axes of all pseudo-Anosov braids are strongly contracting. More generally, we consider a Garside group $G$ of finite type with cyclic center. We prove that in the Cayley graph of $G/Z(G)$, equipped with the Garside generators, the axis of any Morse element is strongly contracting. As a consequence, we prove that Morse elements act loxodromically on the additional length graph of $G$.

Dates et versions

hal-03273228 , version 1 (29-06-2021)

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Matthieu Calvez, Bert Wiest. Morse elements in Garside groups are strongly contracting. 2021. ⟨hal-03273228⟩
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