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Quotients of braid groups by their congruence subgroups (2209.09889v2)
Published 20 Sep 2022 in math.GR, math.AT, math.GT, and math.RT
Abstract: The congruence subgroups of braid groups arise from a congruence condition on the integral Burau representation $B_n \to \operatorname{GL}{n}(\mathbb Z)$. We find the image of such congruence subgroups in $\operatorname{GL}{n}(\mathbb Z)$-an open problem posed by Dan Margalit. Additionally, we characterize the quotients of braid groups by their congruence subgroups in terms of symplectic congruence subgroups.
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