Artin groups of infinite type: trivial centers and acylindical hyperbolicity

Abstract

While finite type Artin groups and right-angled Artin groups are well-understood, little is known about more general Artin groups. In this paper we use the action of an infinite type Artin group $A_{\Gamma }$ on a CAT(0) cube complex to prove that $A_{\Gamma }$ has trivial center providing the graph $\Gamma$ is not the star of a single vertex, and is acylindrically hyperbolic providing $\Gamma$ is not a join.

15 pages, 4 figures. June 1 2018-minor revisions and added references