The $K(\pi ,1)$ conjecture for a class of Artin groups

Abstract

Salvetti constructed a cellular space $B_D$ for any Artin group $A_D$ defined by a Coxeter graph $D$. We show that $B_D$ is an Eilenberg–Mac Lane space if $B_{D^{\prime }}$ is an Eilenberg–Mac Lane space for every subgraph $D^{\prime }$ of $D$ involving no $\infty$-edges.