Séance Séminaire

Séminaire Gaston Darboux

Algebraic and Topological Aspects of Virtual Artin Groups

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 an algebraic and group-theoretic point of view, 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. Additionally, we will briefly discuss some topological aspects of these fascinating groups. In particular, 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.