On the Burau representation of $B_3$ modulo $p$

Donsung Lee

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arXiv · 2406.14538

On the Burau representation of $B_3$ modulo $p$

Donsung Lee

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Abstract

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 $p$.

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Donsung Lee. 2024-06-20. On the Burau representation of $B_3$ modulo $p$. https://arxiv.org/abs/2406.14538

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