Quotients of braid groups by their congruence subgroups

Wade Bloomquist; Peter Patzt; Nancy Scherich

doi:10.1090/bproc/200

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Quotients of braid groups by their congruence subgroups

Journal article

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Quotients of braid groups by their congruence subgroups

Wade Bloomquist, Peter Patzt and Nancy Scherich

Proceedings of the American Mathematical Society. Series B, Vol.11(45), pp.508-524

10/18/2024

DOI: 10.1090/bproc/200

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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.

Research article

Details

Title: Subtitle: Quotients of braid groups by their congruence subgroups
Creators: Wade Bloomquist - University of Iowa
Peter Patzt - University of Oklahoma
Nancy Scherich - Elon University
Resource Type: Journal article
Publication Details: Proceedings of the American Mathematical Society. Series B, Vol.11(45), pp.508-524
DOI: 10.1090/bproc/200
ISSN: 2330-1511
eISSN: 2330-1511
Publisher: American Mathematical Society
Number of pages: 17
Language: English
Date published: 10/18/2024
Academic Unit: Mathematics
Record Identifier: 9984936506002771

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