In this talk we will show the state of the art of the connection between crystallographic groups and generalized braid groups (surface and virtual braids, virtual twins and others). The relation between braid theory and crystallographic groups is currently a subject of great interest, initially established for Artin’s braid groups, and considerable progress has been made in recent years. We shall give more details for the case of virtual braid groups.

https://indico.math.cnrs.fr/event/10330/