Congruence Subgroups of the Virtual Braid Group

Wade Bloomquist; Alexa Goldberg; Nancy Scherich

doi:10.1142/S0218216526500264

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Congruence Subgroups of the Virtual Braid Group

Journal article

Peer reviewed

Congruence Subgroups of the Virtual Braid Group

Wade Bloomquist, Alexa Goldberg and Nancy Scherich

Journal of knot theory and its ramifications

03/13/2026

DOI: 10.1142/S0218216526500264

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Abstract

We extend the notion of congruence subgroups of the braid group to the virtual braid group using an extension of the integral Burau representation. We prove that the level 2 congruence subgroup of the virtual braid group is the pure virtual braid group, recovering a virtual analogue of a result of Arnol’d. We pose several questions which highlight the difference between the classical and virtual braid groups.

Braid groups

virtual braid groups

Burau representation

congruence subgroups

Details

Title: Subtitle: Congruence Subgroups of the Virtual Braid Group
Creators: Wade Bloomquist
Alexa Goldberg
Nancy Scherich - Twitter (United States)
Resource Type: Journal article
Publication Details: Journal of knot theory and its ramifications
DOI: 10.1142/S0218216526500264
ISSN: 0218-2165
eISSN: 1793-6527
Publisher: World Scientific
Grant note: AMS-Simons: DMS-2532699
No Statement Available
Language: English
Electronic publication date: 03/13/2026
Academic Unit: Mathematics
Record Identifier: 9985147196202771

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