The $K(\pi, 1)$ conjecture for Artin groups of spherical type

Let $W$ be a Coxeter group, let $G_W$ be its associated Artin group, and let

$$Y_W = \left( (I + iV) \setminus \bigcup_r H_r \otimes_\mathbb{R} \mathbb{C} \right) / W$$

be the orbit configuration space, where $I$ is the Tits cone in the real reflection representation $V$, and $H_r \otimes \mathbb{C}$ is the complexified reflection hyperplane associated with a reflection $r \in W$. The $K(\pi, 1)$ conjecture. For every Coxeter group $W$, we have

$$Y_W \simeq K(G_W,1).$$

For symmetric groups this recovers the fact that unordered configurations of distinct points in $\mathbb{C}$ classify the braid group. The claim was proved by Salvetti, whose resulting model is known as the Salvetti complex.