4 problems

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The K(pi,1) conjecture for complex reflection arrangements
Let $V$ be a finite-dimensional complex vector space, let $W\subset \operatorname{GL}(V)$ be a finite complex reflection group, and let $V^{\operatorname{reg}}$ be the complement i…
Conjecturesolvedcomplex-reflection-groups kpi1-spaces reflection-arrangementsarXiv posted 2 days ago
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The quasi-center conjecture for zigzag 6-cycles in type $D_n$ Artin complexes
Let $\Lambda$ be the Dynkin diagram of type $D_n$ , and let $\Delta_\Lambda$ be its associated Artin complex. Order the vertex types by…
Conjectureopenartin-groups kpi1-spaces type-darXiv posted 2 days ago
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The admissible-cycle filling complexity conjecture for spherical Artin complexes
Let $A_S$ be an irreducible spherical Artin group, let $\Delta_S$ be its associated Artin complex, and let $\mathsf C_S$ be its associated Coxeter complex with the natural action o…
Conjectureopenartin-groups coxeter-complexes kpi1-spacesarXiv posted 2 days ago
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The Arnol'd–Brieskorn–Pham–Thom $K(\pi,1)$ conjecture for Artin arrangement complements
Artin groups arise as fundamental groups of certain complex hyperplane arrangement complements. Arnol'd–Brieskorn–Pham–Thom $K(\pi,1)$ conjecture. These arrangement complements are…
Conjectureopenartin-groups hyperplane-arrangements kpi1-spacesarXiv posted 2 days ago

The K(pi,1) conjecture for complex reflection arrangements