A generalisation of the Burau representation and groups $G_{n}^{3}$ for classical braids

Vassily Olegovich Manturov; Igor Mikhailovich Nikonov

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arXiv · 2602.07890

A generalisation of the Burau representation and groups $G_{n}^{3}$ for classical braids

Vassily Olegovich Manturov·Igor Mikhailovich Nikonov

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Abstract

We consider a certain modification of the group $G^3_n$ which describes dynamics of point configurations, in particular braids, and define a representation of the modified $G^3_n$. The braid representation induced is powerful enough to detect the kernel of the Burau representation.

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Vassily Olegovich Manturov, Igor Mikhailovich Nikonov. 2026-02-08. A generalisation of the Burau representation and groups $G_{n}^{3}$ for classical braids. https://arxiv.org/abs/2602.07890

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