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arXiv · 1905.11032

XXL type Artin groups are CAT(0) and acylindrically hyperbolic

Thomas Haettel
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Abstract

We describe a simple locally CAT(0) classifying space for extra extra large type Artin groups (with all labels at least 5). Furthermore, when the Artin group is not dihedral, we describe a rank 1 periodic geodesic, thus proving that extra large type Artin groups are acylindrically hyperbolic. Together with Property RD proved by Ciabonu, Holt and Rees, the CAT(0) property implies the Baum-Connes conjecture for all XXL type Artin groups.

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Thomas Haettel. 2019-05-27. XXL type Artin groups are CAT(0) and acylindrically hyperbolic. https://arxiv.org/abs/1905.11032

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