10 problems

Let $A_S$ be an Artin group, and let $S'ubset S$ be almost spherical. Let $\Delta_{S,S'}$ denote the relative Artin complex spanned by vertices of types indexed by $S'$. Assume tha…

Let $A$ be an Artin group, and let the canonical complex manifold associated to $A$ be the space under consideration. The $K(\pi,1)$-conjecture. This manifold is aspherical. The co…

Let $W$ be a Coxeter group acting on its reflection representation, let $\Theta=V^*$, and let $\operatorname{Cone}\subseteq\Theta$ be its Tits cone with interior…

Let $A$ be an Artin group and let $M$ be the complement of the associated hyperplane arrangement, whose fundamental group is $A$. The $K(\pi,1)$ conjecture. The space $M$ is an Eil…

Let $\Lambda$ and $\Lambda'$ satisfy the assumptions of the source's six-cycle link lemma, with $\Lambda'$ not necessarily admissible in $\Lambda$. Consider the links of vertices i…

Let $G$ be a path graph or one of the graphs $\Delta_{n,1}$ for $n\ge 2$, and let $\mathcal{A}_G$ denote its connected subgraph arrangement. K(pi,1) conjecture. The arrangement…

The $K(\pi,1)$-conjecture. The orbit space $\mathcal H(W)/W$ is a $K(\pi,1)$ for the Artin group $A$ associated to $W$.

Let $W$ be a Coxeter group acting on its Tits cone $I\subseteq\mathbb{R}^n$, and let $\mathcal{A}$ be the set of fixed hyperplanes of reflections of $W$. Define … The $K(\pi, 1)$ c…

Artin groups' algebraic and $K(\pi,1)$ conjectures. For every Artin group $A_{\Gamma}$: (1) $A_{\Gamma}$ has solvable word and conjugacy problems; (2) $A_{\Gamma}$ is torsion-free;…

The $K(\pi,1)$-conjecture for Artin groups. The $K(\pi,1)$-Question has a positive answer for every Artin poset $A\mathcal{S}(L)$; equivalently,