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arXiv · 2405.16607

Salter's question on the image of the Burau representation of $B_3$

Donsung Lee
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Abstract

In 1974, Birman posed the question of under what conditions a matrix with Laurent polynomial entries is in the image of the Burau representation. In 1984, Squier observed that the matrices in the image are contained in a unitary group. In 2021, Salter formulated a specific question: whether the central quotient of the Burau image group is the central quotient of a certain subgroup of the unitary group. We solve this question negatively in the simplest nontrivial case, $n=3$, algorithmically constructing a counterexample.

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Donsung Lee. 2024-05-26. Salter's question on the image of the Burau representation of $B_3$. https://arxiv.org/abs/2405.16607

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