On the Burau representation of $B_3$ modulo $p$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911927878287360 |
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| author | Lee, Donsung |
| author_facet | Lee, Donsung |
| contents | We present an algorithm that, given a prime $p$ as input, determines whether or not the Burau representation of the 3-strand braid group modulo $p$ is faithful. We also prove that the representation is indeed faithful when $p\le 13$. Additionally, we re-pose Salter's question on the Burau representation of $B_3$ over finite fields $\mathbb{F}_p$, and solve it for every $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14538 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Burau representation of $B_3$ modulo $p$ Lee, Donsung Geometric Topology Group Theory 20F36, 20H05, 20E05, 20E06, 14H52 We present an algorithm that, given a prime $p$ as input, determines whether or not the Burau representation of the 3-strand braid group modulo $p$ is faithful. We also prove that the representation is indeed faithful when $p\le 13$. Additionally, we re-pose Salter's question on the Burau representation of $B_3$ over finite fields $\mathbb{F}_p$, and solve it for every $p$. |
| title | On the Burau representation of $B_3$ modulo $p$ |
| topic | Geometric Topology Group Theory 20F36, 20H05, 20E05, 20E06, 14H52 |
| url | https://arxiv.org/abs/2406.14538 |