Acylindrical Hyperbolicity Conjecture for irreducible Artin groups

Let AΓA_\Gamma be an irreducible Artin group, and let Z(AΓ)Z(A_\Gamma) denote its centre. The central quotient is AΓ/Z(AΓ)A_\Gamma/Z(A_\Gamma). Acylindrical Hyperbolicity Conjecture. The group

AΓ/Z(AΓ)A_\Gamma/Z(A_\Gamma)

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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