The acylindrical hyperbolicity conjecture for Artin groups

Let ASA_S be an Artin group, and let ZSZ_S denote the centre of ASA_S. Acylindrical hyperbolicity conjecture. The quotient AS/ZSA_S/Z_S is acylindrically hyperbolic. This would provide a broad criterion for acylindrical hyperbolicity among Artin groups, a property that remains open in general.

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Primary source

William D. Cohen, “Acylindrical Visual Splittings and The Tits Alternative For Artin Groups”, arXiv:2509.03305 (2025).

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