English

Quotients of braid groups by their congruence subgroups

Group Theory 2023-06-13 v2 Algebraic Topology Geometric Topology Representation Theory

Abstract

The congruence subgroups of braid groups arise from a congruence condition on the integral Burau representation BnGLn(Z)B_n \to \operatorname{GL}_{n}(\mathbb Z). We find the image of such congruence subgroups in GLn(Z)\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.

Keywords

Cite

@article{arxiv.2209.09889,
  title  = {Quotients of braid groups by their congruence subgroups},
  author = {Wade Bloomquist and Peter Patzt and Nancy Scherich},
  journal= {arXiv preprint arXiv:2209.09889},
  year   = {2023}
}

Comments

Important correction: The previous version incorrectly used the reduced Burau representation

R2 v1 2026-06-28T01:45:38.845Z