New Garside structures and applications to Artin groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914974289362944 |
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| author | Haettel, Thomas Huang, Jingyin |
| author_facet | Haettel, Thomas Huang, Jingyin |
| contents | Garside groups are combinatorial generalizations of braid groups which enjoy many nice algebraic, geometric, and algorithmic properties. In this article we propose a method for turning the direct product of a group $G$ by $\mathbb{Z}$ into a Garside group, under simple assumptions on $G$. This method gives many new examples of Garside groups, including groups satisfying certain small cancellation condition (including surface groups) and groups with a systolic presentation.
Our method also works for a large class of Artin groups, leading to many new group theoretic, geometric and topological consequences for them. In particular, we prove new cases of $K(π,1)$-conjecture for some hyperbolic type Artin groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_11622 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New Garside structures and applications to Artin groups Haettel, Thomas Huang, Jingyin Group Theory Geometric Topology 20E42, 20F36, 20F55, 05B35, 06A12, 20F65, 05C25 Garside groups are combinatorial generalizations of braid groups which enjoy many nice algebraic, geometric, and algorithmic properties. In this article we propose a method for turning the direct product of a group $G$ by $\mathbb{Z}$ into a Garside group, under simple assumptions on $G$. This method gives many new examples of Garside groups, including groups satisfying certain small cancellation condition (including surface groups) and groups with a systolic presentation. Our method also works for a large class of Artin groups, leading to many new group theoretic, geometric and topological consequences for them. In particular, we prove new cases of $K(π,1)$-conjecture for some hyperbolic type Artin groups. |
| title | New Garside structures and applications to Artin groups |
| topic | Group Theory Geometric Topology 20E42, 20F36, 20F55, 05B35, 06A12, 20F65, 05C25 |
| url | https://arxiv.org/abs/2305.11622 |