4 problems

Let $A_\Gamma$ be an infinite-type Artin group, and let $D_\Gamma$ be its Deligne complex, whose vertices are cosets $aA_T$ of spherical-type standard parabolic subgroups and whose…

Let $A_S$ be a spherical Artin group, and let $\Delta_S$ be its spherical Deligne complex, equipped with its naturally defined metric. Charney–Davis conjecture. The complex…

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…

Let $A_S$ be an Artin group of type $A_n$, let $\pi:\Delta_S\to\mathsf C_S$ be the folding map to the Coxeter complex, let $H$ be a wall in $\mathsf C_S$, and let $K_H$ be the maxi…