Generators for the level $m$ congruence subgroups of braid groups

Abstract

We prove for $m\ge 1$ and $n\ge 5$ 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.

12 pages, 0 figures