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Acylindrical
hyperbolicity for Artin groups with a visual splitting
Ruth Charney, Alexandre Martin and Rose Morris-Wright |
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Algebraic & Geometric Topology 26 (2026) 1507–1528
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DOI: 10.2140/agt.2026.26.1507
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Abstract |
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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. |
Keywords
Artin groups, acylindrical hyperbolicity, groups acting on
trees
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Mathematical Subject Classification
Primary: 20F65
Secondary: 20F36, 20F67
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References |
Publication
Received: 27 May 2024
Revised: 10 March 2025
Accepted: 15 April 2025
Published: 25 April 2026
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Authors |
| Ruth Charney | |
| Department of Mathematics Brandeis University Waltham, MA United States |
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| Alexandre Martin | |
| Department of Mathematics and the
Maxwell Institute for the Mathematical Sciences Heriot-Watt University Edinburgh United Kingdom |
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| Rose Morris-Wright | |
| Department of Mathematics Middlebury College Middlebury, VT United States |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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