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

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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Veröffentlicht in:arXiv.org 2024-09
Hauptverfasser: Banerjee, Ishan, Huxford, Peter
Format: Artikel
Sprache:eng
Schlagworte:
Braid theory
Braiding
Subgroups
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Zusammenfassung: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