The $K(\pi,1)$-conjecture for infinite Coxeter groups

Let $W$ be an infinite Coxeter group, let $Y_W$ be the associated hyperplane complement in $\mathbb{C}\otimes V$ restricted to the Tits cone, and let $A$ be the associated Artin group. For finite Coxeter groups, Deligne's theorem states that $Y_W/W$ is an aspherical space with fundamental group $A$. The $K(\pi,1)$-conjecture. The analogue of Deligne's theorem holds for infinite Coxeter groups; in particular, $Y_W/W$ is aspherical and has fundamental group $A$. Part of the conjecture, namely $A=\pi_1(Y_W/W)$, is known for arbitrary Coxeter groups, and asphericity has been proved for some classes of infinite Coxeter groups, but the conjecture remains open for arbitrary Coxeter groups.