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Classifying spaces and geometric obstructions for Artin groups
The Salvetti complex of every finite-rank Artin group is aspherical, proving the Artin conjecture. Arbitrary intersections of its parabolic subgroups are parabolic, proving the Parabolic Intersection Conjecture. An explicit Artin group admits no proper cocompact isometric action on any nonempty proper CAT space.
Manuscripts in this family · 3
Harmonic heights and the Artin K(pi,1) conjecture
Sep 23, 2026·paper.pdfLean
We prove that the standard Salvetti complex of every Artin group with finitely many standard generators is aspherical. This resolves the Artin conjecture in finite rank.
An Artin group with no geometric CAT(0) action
Sep 23, 2026·paper.pdfLean
We construct an Artin group on 116 generators that admits no proper, cocompact isometric action on a nonempty proper CAT(0) space. This refutes the CAT(0) conjecture for Artin groups.
Parabolic intersections in Artin groups
Sep 23, 2026·paper.pdf
We prove that every intersection of parabolic subgroups of any finite-rank Artin group, with arbitrary finite or infinite Coxeter labels, is parabolic. This resolves the Parabolic Intersection Conjecture affirmatively.