Artin groups of infinite type: Trivial centers and acylindrical hyperbolicity

Charney, Ruth; Morris-Wright, Rose

doi:10.1090/proc/14503

Artin groups of infinite type: Trivial centers and acylindrical hyperbolicity
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by Ruth Charney and Rose Morris-Wright PDF

Proc. Amer. Math. Soc. 147 (2019), 3675-3689 Request permission

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 $\Gamma$ is not the star of a single vertex, and is acylindrically hyperbolic providing $\Gamma$ is not a join.

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