From Trees to Tripods: Proof of $K(\pi ,1)$ for Artin groups with $ABI$-type spherical parabolics

Nima Hoda, Jingyin Huang

We reduce the $K(\pi ,1)$-conjecture for all Artin groups with tree Coxeter diagrams to properties of Artin groups with tripod-shaped Coxeter diagrams. Combining this reduction theore…