Artin groups of infinite type: trivial centers and acylindical hyperbolicity

Ruth Charney; Rose Morris-Wright

Artin groups of infinite type: trivial centers and acylindical hyperbolicity

Group Theory 2018-06-04 v2

Authors: Ruth Charney , Rose Morris-Wright

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.

Keywords

artin groups infinite type trivial center acylindrical hyperbolicity cat(0) cube complex

Cite

@article{arxiv.1805.04028,
  title  = {Artin groups of infinite type: trivial centers and acylindical hyperbolicity},
  author = {Ruth Charney and Rose Morris-Wright},
  journal= {arXiv preprint arXiv:1805.04028},
  year   = {2018}
}

Comments

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

Artin groups of infinite type: trivial centers and acylindical hyperbolicity

Abstract

Keywords

Cite

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