10 problems

Let $\Gamma$ be a finite simplicial graph with labeling map $l:E(\Gamma)\to\{2,3,4,\dots\}$, let $A_\Gamma$ be its Artin group, and let $\mathcal{P}$ be the poset of spherical spec…

Let $A_S$ be an Artin group whose Coxeter diagram is a tree. A vertex of the Artin complex $\Delta_S$ is of type $\hat s=S\setminus\{s\}$ if it corresponds to a coset of the form…

Labeled 4-wheel conjecture. The Artin complex $\Delta_{\Lambda}$ satisfies the labeled 4-wheel condition.

Let $\Gamma$ be a finite simplicial graph with edges labeled by finite integers at least $2$, let $A_\Gamma$ be the associated Artin group, and let $W_\Gamma$ be its associated Cox…

Artin group $K(\pi,1)$ conjecture. Every Artin group satisfies the $K(\pi,1)$ conjecture.

Let $A$ be an irreducible Artin group of euclidean type, and let $B A$ be the classifying space constructed in the paper. Let $M$ be the standard topological space with fundamental…

Let $G(S)$ be an Artin group, and consider the corresponding hyperplane-arrangement analogue. The hyperplane-arrangement formulation of the K(π,1)-conjecture. The hyperplane-arrang…

Let $G(S)$ be an Artin group associated to a Coxeter system with generating set $S$. Let $S^f$ denote the poset of spherical subsets of $S$, and let $N(S^f\int G(-))$ be the nerve…

$K(\pi,1)$ conjecture. For every Coxeter graph $\Gamma$, the quotient

Artin-group $K(\pi,1)$ conjecture. Such orbit spaces are always $K(\pi,1)$ spaces.