3 problems

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Brieskorn's $K(\pi,1)$ conjecture for complexified real reflection arrangements
Let $V$ be a finite-dimensional complex vector space, let $W\subseteq \operatorname{GL}(V)$ be a finite complex reflection group, and let $V^{\operatorname{reg}}$ be the complement…
Conjecturesolvedcomplex-reflection-groups hyperplane-arrangements kpi1arXiv posted 2 days ago
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Saito's conjecture for hyperpolygonal arrangements
Let ${\mathscr H}_n$ be the hyperpolygonal arrangement in ${\mathbb R}^n$ , and let a complexified arrangement mean the arrangement obtained by extending its defining real hyperplan…
Conjectureopenfree-arrangements hyperplane-arrangements kpi1arXiv posted 2 days ago
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The $K(\pi,1)$ -Conjecture for Artin groups
The $K(\pi,1)$ -Conjecture. The quotient $Y_W/W$ is aspherical with fundamental group $A$ ; equivalently, it is a $K(A,1)$ space.
Conjectureopenartin-groups geometric-group-theory kpi1arXiv posted 2 days ago

Brieskorn's K(π,1)K(\pi,1)K(π,1) conjecture for complexified real reflection arrangements