CAT(0) cube complex for virtual Artin groups

par M. José Gálvez Mateos (Instituto de Matemáticas de la Universidad de Sevilla (IMUS) and Departamento de Álgebra, Universidad de Sevilla, Spain.)

vendredi 2 oct. 2026, 14:00 → 15:00 Europe/Paris

Salle de séminaire (Orléans institut Denis Poisson)

Abstract: 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.