Acylindrical hyperbolicity for Artin groups with a visual splitting

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Authors: Ruth M. Charney, Alexandre Martin, Rose Morris-Wright
Cited by: 0

Abstract

We establish a criterion that implies the acylindrical hyperbolicity of many Artin groups admitting a visual splitting. This gives a variety of new examples of acylindrically hyperbolic Artin groups, including many Artin groups of FC-type. Our approach relies on understanding when parabolic subgroups are weakly malnormal in a given Artin group. We formulate a conjecture for when this happens, and prove it for several classes of Artin groups, including all spherical-type, all two-dimensional, and all even FC-type Artin groups. In addition, we establish some connections between several conjectures about Artin groups, related to questions of acylindrical hyperbolicity, weak malnormality of parabolic subgroups, and intersections of parabolic subgroups.

Fields of Study & Subjects

Geometric and Algebraic Topology

Publication details

Journal / source
Algebraic & Geometric Topology
Volume
26
Issue
4
Pages
1507–1528
Publication date
25 April 2026
Language
EN