Acylindrical hyperbolicity and the centers of Artin groups that are not free of infinity

Motoko Kato, Shin-ichi Oguni

Published 2024-06-02Version 1

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 the actions on them. The authors developed their study and clarified when acylindrical hyperbolicity holds for Artin groups of infinite type associated with graphs that are not cones. In this paper, we introduce reduced clique-cube complexes. By using them, we show acylindrical hyperbolicity of irreducible Artin groups associated with graphs that are not cliques, that is, irreducible Artin groups that are not free of infinity. Such Artin groups contain infinite type Artin groups of type FC. As an application, we see that the centers of such Artin groups are finite, and that actually they are trivial in many cases.