Two-dimensional Artin groups with CAT(0) dimension three.

DOI10.1023/A:1020962804856zbMath1070.20043arXivmath/0012102OpenAlexW3002901560MaRDI QIDQ1855285

Noel Brady, John Crisp

Publication date: 4 February 2003

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0012102

zbMATH Keywords

group actionsArtin groupsnon-positive curvaturecohomological dimensiondiscrete groupslength functionstopological dimensiontwo-dimensional complexes

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) Hyperbolic groups and nonpositively curved groups (20F67) Group actions on manifolds and cell complexes in low dimensions (57M60)

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The 6-strand braid group is \(\mathrm{CAT}(0)\). ⋮ Cubulation of some triangle-free Artin groups ⋮ An introduction to right-angled Artin groups. ⋮ Automorphisms and abstract commensurators of 2-dimensional Artin groups. ⋮ The \(\text{FA}_n\) conjecture for Coxeter groups. ⋮ Lower bounds on cubical dimensionof $C’(1/6)$ groups ⋮ Parabolic isometries of CAT(0) spaces and CAT(0) dimensions. ⋮ On the classification of CAT(0) structures for the 4-string braid group. ⋮ Relative hyperbolicity and Artin groups. ⋮ Helly meets Garside and Artin ⋮ Metric systolicity and two-dimensional Artin groups ⋮ Acylindrical hyperbolicity for Artin groups of dimension \(2\) ⋮ XXL type Artin groups are CAT(0) and acylindrically hyperbolic ⋮ Three-dimensional FC Artin groups are CAT(0). ⋮ On the \(\text{CAT}(0)\) dimension of 2-dimensional Bestvina-Brady groups.

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