Abstract

Virtual Artin groups were introduced a few years ago by Bellingeri, Paris, and Thiel with the aim of generalizing the well-studied structure of virtual braids to all Artin groups. In this talk, we will present two possible perspectives for studying these groups: an algebraic one and a topological one. From a topological point of view, we will explore the construction of K(π,1) spaces for certain subgroups of virtual Artin groups, linking them to a famous conjecture and existing constructions. By an algebraic/group theoretic approach, we will investigate the rigidity of these groups, specifically addressing the question of whether they can be decomposed into a direct product of two proper subgroups. The answer to this question provides interesting insights into the automorphism groups of these structures.