Generators for the level $m$ congruence subgroups of braid groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913500366897152 |
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| author | Banerjee, Ishan Huxford, Peter |
| author_facet | Banerjee, Ishan Huxford, Peter |
| contents | We prove for $m\geq1$ and $n\geq5$ that the level $m$ congruence subgroup $B_n[m]$ of the braid group $B_n$ associated to the integral Burau representation $B_n\to\mathrm{GL}_n(\mathbb{Z})$ is generated by $m$th powers of half-twists and the braid Torelli group. This solves a problem of Margalit, generalizing work of Assion, Brendle--Margalit, Nakamura, Stylianakis and Wajnryb. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generators for the level $m$ congruence subgroups of braid groups Banerjee, Ishan Huxford, Peter Group Theory Geometric Topology We prove for $m\geq1$ and $n\geq5$ that the level $m$ congruence subgroup $B_n[m]$ of the braid group $B_n$ associated to the integral Burau representation $B_n\to\mathrm{GL}_n(\mathbb{Z})$ is generated by $m$th powers of half-twists and the braid Torelli group. This solves a problem of Margalit, generalizing work of Assion, Brendle--Margalit, Nakamura, Stylianakis and Wajnryb. |
| title | Generators for the level $m$ congruence subgroups of braid groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2409.09612 |