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arXiv · 1805.04028

Artin groups of infinite type: trivial centers and acylindical hyperbolicity

Ruth Charney·Rose Morris-Wright
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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.

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Ruth Charney, Rose Morris-Wright. 2018-05-10. Artin groups of infinite type: trivial centers and acylindical hyperbolicity. https://arxiv.org/abs/1805.04028

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