GT ADG-Systèmes Dynamiques

CAT(0) cube complex for virtual Artin groups
José Gálvez Mateos (Instituto de Matemáticas de la Universidad de Sevilla (IMUS) and Departamento de Álgebra, Universidad de Sevilla, Spain.)
Friday 02 October 2026 14:00 -  Orléans institut Denis Poisson -  Salle de séminaire

Résumé :

Virtual Artin groups, recently introduced as a natural generalization of virtual braid groups, unify the structure of Artin-Tits groups and Coxeter groups through mixed interaction relations. In this talk, we construct a geometric object for studying these groups: a cellular complex endowed with a natural cube complex structure $\Xi_{\mathcal{D}}$, associated with any elemental complex $\mathcal{D}$.   We prove that $\Xi_{\mathcal{D}}$ is connected, simply connected, and locally regular. The virtual Artin group acts on $\Xi_{\mathcal{D}}$ regularly, cocompactly, and by isometries, with cell stabilizers given precisely by parabolic subgroups. Finally, we characterize the metric properties of this space, showing that $\Xi_{\mathcal{D}}$ is non-positively curved in the sense of CAT(0) if and only if $\mathcal{D}$ is a flag complex.

Liens :

• Indico