Acylindrical hyperbolicity of Artin groups associated with graphs that are not cones

TL;DR

This paper extends the class of Artin groups known to be acylindrically hyperbolic by analyzing their associated graphs and actions on clique-cube complexes, broadening previous results.

Contribution

It generalizes acylindrical hyperbolicity results to Artin groups linked with graphs that are not cones, beyond the previously studied non-join graphs.

Findings

Proves acylindrical hyperbolicity for a broader class of Artin groups.

Develops new techniques for analyzing group actions on complexes.

Extends previous theoretical frameworks to more general graph structures.

Abstract

Charney and Morris-Wright showed acylindrical hyperbolicity of Artin groups of infinite type associated with graphs that are not joins, by studying clique-cube complexes and actions on them. In this paper, by developing their study and formulating some additional discussion, we demonstrate that acylindrical hyperbolicity holds for more general Artin groups. Indeed, we are able to treat Artin groups of infinite type associated with graphs that are not cones.