Séminaires : Groupes, Représentations et Géométrie

Le séminaire de l'équipe GRG. SI vous n'êtes pas membre de l'équipe mais souhaitez recevoir les informations, abonnez vous à la liste https://listes.services.cnrs.fr/wws/info/sem-gr.paris

In his proof of the $K(\pi,1)$ conjecture for complex reflection arrangements, Bessis introduced new Garside structures useful for handling irreducible complex braid groups. A particularly tough case to study is that of the Borchardt braid group $B(G_{31})$, for which a Garside category is needed (instead of just a Garside monoid).

In this talk I will explain how to use this Garside category to prove several group-theoretic results on $B(G_{31})$. Some of these results are new, and others were obtained before using non-Garside arguments.

If time permits, I will also give some details regarding the topological construction of this category, and the way it can be used to understand the parabolic subgroups of $B(G_{31})$, as defined by Marin and González-Meneses