Acylindrical hyperbolicity for Artin groups with a visual splitting
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