Artin groups of infinite type: Trivial centers and acylindrical 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 Γ A_{\Gamma } on a CAT(0) cube complex to prove that A Γ A_{\Gamma } has trivial center providing Γ \Gamma is not the star of a single vertex, and is acylindrically hyperbolic providing Γ \Gamma is not a join.