Congruence Subgroups of the Virtual Braid Group

Key Points

• This research aims to understand the extensions of congruence subgroups in the context of virtual braid groups.
• Extension of the integral Burau representation to the virtual braid group
• Proving the correspondence between level 2 congruence subgroup and pure virtual braid group
• The level 2 congruence subgroup of the virtual braid group is identified as the pure virtual braid group
• The findings recover a virtual analogue of a classical result by Arnol’d
• Questions are posed to underline differences between classical and virtual braid groups.