Acylindrical Visual Splittings and The Tits Alternative For Artin Groups

2025/09/03 by Cohen, William D.
#20E08 (Secondary) #20F36 (Primary) #20F67 (Primary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2509.03305

Abstract

We give a necessary and sufficient condition on a visual splitting of an Artin group satisfying the conditions of two well known conjectures to be acylindrical, and demonstrate how this can be used to provide a large class of novel examples of Artin groups that satisfy the Tits alternative.

Citations

• JSJ splittings for all Artin groups
• Combination theorems for Wise's power alternative
• Acylindrical hyperbolicity for Artin groups with a visual splitting
• Groups Acting Acylindrically on Trees
• The Tits Alternative for two-dimensional Artin groups and Wise's Power Alternative
• Parabolic subgroups inside parabolic subgroups of Artin groups
• On parabolic subgroups of Artin groups
• Parabolic subgroups of two-dimensional Artin groups and systolic-by-function complexes
• Acylindrical hyperbolicity for Artin groups of dimension 2
• Tits alternative for Artin groups of type FC
• Acylindrical actions for two-dimensional Artin groups of hyperbolic type
• Groups acting acylindrically on hyperbolic spaces
• Virtually cocompactly cubulated Artin-Tits groups
• Acylindrically hyperbolic groups
• On accessibility of finitely generated groups
• The Tits alternative for CAT(0) cubical complexes
• Linearity of Artin groups of finite type
• The Tits Alternative for Out(F_n) II: A Kolchin Type Theorem
• Artin-Gruppen und Coxeter-Gruppen

Related

• Acylindrical hyperbolicity for Artin groups with a visual splitting
• Acylindrical hyperbolicity of Artin groups associated with graphs that are not cones
• A conjecture about Artin-Tits groups
• Around subgroups of Artin groups: derived subgroups and acylindrical hyperbolicity in the even FC-case
• Double centralizers in Artin-Tits groups