On the Burau Representation of $B_4$ modulo $p$

A. Beridze; S. Bigelow; P. Traczyk

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arXiv · 1904.11730

On the Burau Representation of $B_4$ modulo $p$

A. Beridze·S. Bigelow·P. Traczyk

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Abstract

The problem of faithfulness of the (reduced) Burau representation for $n =4$ is known to be equivalent to the problem of whether certain two matrices $A$ and $B$ generate a free group of rank two. It is known that $A^3$ and $B^3$ generate a free group of rank two \cite{9}, \cite{10}, \cite{4}. We prove that they also generate a free group when considered as matrices over the $\mathbb{Z}_p[t,t^{-1}]$ for any integer $p > 1$.

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BibTeX RIS

A. Beridze, S. Bigelow, P. Traczyk. 2019-04-26. On the Burau Representation of $B_4$ modulo $p$. https://arxiv.org/abs/1904.11730

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