Generators for the level \(m\) congruence subgroups of braid groups

We prove for \(m\geq1\) and \(n\geq5\) that the level \(m\) congruence subgroup \(B_n[m]\) of the braid group \(B_n\) associated to the integral Burau representation \(B_n\to\mathrm{GL}_n(\mathbb{Z})\) is generated by \(m\)th powers of half-twists and the braid Torelli group. This solves a problem o...

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Bibliographic Details
Published inarXiv.org
Main Authors Banerjee, Ishan, Huxford, Peter
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.09.2024
Subjects
Braid theory
Braiding
Subgroups
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Summary:We prove for \(m\geq1\) and \(n\geq5\) that the level \(m\) congruence subgroup \(B_n[m]\) of the braid group \(B_n\) associated to the integral Burau representation \(B_n\to\mathrm{GL}_n(\mathbb{Z})\) is generated by \(m\)th powers of half-twists and the braid Torelli group. This solves a problem of Margalit, generalizing work of Assion, Brendle--Margalit, Nakamura, Stylianakis and Wajnryb.
ISSN:2331-8422