Congruence Subgroups of the Virtual Braid Group
Geometric Topology
2025-10-27 v1
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.
Keywords
Cite
@article{arxiv.2510.21593,
title = {Congruence Subgroups of the Virtual Braid Group},
author = {Wade Bloomquist and Alexa Goldberg and Nancy Scherich},
journal= {arXiv preprint arXiv:2510.21593},
year = {2025}
}