Morse elements in Garside groups are strongly contracting
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866912167568080896 |
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| author | Calvez, Matthieu Wiest, Bert |
| author_facet | Calvez, Matthieu Wiest, Bert |
| contents | 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 $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_14826 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Morse elements in Garside groups are strongly contracting Calvez, Matthieu Wiest, Bert Group Theory Geometric Topology 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 $G$. |
| title | Morse elements in Garside groups are strongly contracting |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2106.14826 |