Acylindrical Hyperbolicity Conjecture for irreducible Artin groups
Acylindrical Hyperbolicity Conjecture for irreducible Artin groups
Let be an irreducible Artin group, and let denote its centre. The central quotient is . Acylindrical Hyperbolicity Conjecture. The group
is acylindrically hyperbolic. This describes the expected acylindrical hyperbolicity of Artin groups after removing the obstruction from their centre: reducible groups split as direct products, while spherical-type groups have an infinite cyclic centre. The central-quotient statement is known for spherical-type Artin groups by work of Calvez and Wiest; the conjecture remains unresolved in the stated generality for irreducible Artin groups.
Sources & referencesView supporting material
Primary source
Ruth Charney, Alexandre Martin and Rose Morris-Wright, “Acylindrical hyperbolicity for Artin groups with a visual splitting”, arXiv:2404.11393 (2024).
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