Congruence Subgroups of the Virtual Braid Group

Wade Bloomquist; Alexa Goldberg; Nancy Scherich

doi:10.48550/arxiv.2510.21593

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Congruence Subgroups of the Virtual Braid Group

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Congruence Subgroups of the Virtual Braid Group

Wade Bloomquist, Alexa Goldberg and Nancy Scherich

ArXiv.org

Cornell University

10/24/2025

DOI: 10.48550/arxiv.2510.21593

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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.

Mathematics - Geometric Topology

Details

Title: Subtitle: Congruence Subgroups of the Virtual Braid Group
Creators: Wade Bloomquist
Alexa Goldberg
Nancy Scherich
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2510.21593
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 10/24/2025
Academic Unit: Mathematics
Record Identifier: 9985019033902771

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