4 problems

Let $\Gamma$ be a Coxeter graph, and let $\mathfrak{cl}^f(\Gamma)$ denote the spherical clique number of $\Gamma$, namely the number of vertices in a maximal spherical clique. A co…

Let $\Gamma$ be a Coxeter graph, let $\mathrm{VA}[\Gamma]$ be the associated virtual Artin group, and let $\iota_{\mathrm{W}}(\mathrm{W}[\Gamma])$ denote its embedded copy of the a…

Let $\Gamma$ be a Coxeter graph and let $\mathrm{A}[\Gamma]$ be the associated Artin group. Artin torsion-freeness conjecture. The Artin group $\mathrm{A}[\Gamma]$ is torsion-free…

Let $\Gamma$ be a Coxeter graph, and let $\mathrm{vD}_{\Gamma}$ be the virtual Deligne complex associated with the virtual Artin group $\mathrm{VA}[\Gamma]$. Equip…