Quotients of braid groups by their congruence subgroups

Wade Bloomquist; Peter Patzt; Nancy Scherich

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arXiv · 2209.09889

Quotients of braid groups by their congruence subgroups

Wade Bloomquist·Peter Patzt·Nancy Scherich

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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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BibTeX RIS

Wade Bloomquist, Peter Patzt, Nancy Scherich. 2022-09-20. Quotients of braid groups by their congruence subgroups. https://arxiv.org/abs/2209.09889

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