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arXiv · 2106.14826

Morse elements in Garside groups are strongly contracting

Matthieu Calvez·Bert Wiest
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Abstract

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 $G$.

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BibTeXRIS

Matthieu Calvez, Bert Wiest. 2021-06-28. Morse elements in Garside groups are strongly contracting. https://doi.org/10.2140/agt.2024.24.4545

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