XXL type Artin groups are CAT(0) and acylindrically hyperbolic
Annales de l'Institut Fourier, Volume 72 (2022) no. 6, pp. 2541-2555.

We describe a simple locally CAT(0) classifying space for XXL 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 XXL type Artin groups are acylindrically hyperbolic. Together with Property RD proved by Ciobanu, Holt and Rees, the CAT(0) property implies the Baum–Connes conjecture for all XXL type Artin groups.

Nous décrivons un espace classifiant localement simple CAT(0) pour les groupes d’Artin de type extra extra large (dont tous les exposants sont au moins égaux à 5). De plus, lorsque le groupe n’est pas diédral, nous décrivons une géodésique périodique de rang 1, ce qui implique que ces groupes d’Artin de type extra extra large sont acylindriquement hyperboliques. En conjonction avec la propriété RD prouvée par Ciobanu, Holt et Rees, cela implique la conjecture de Baum–Connes pour tout les groupes d’Artin de type extra extra large.

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DOI: 10.5802/aif.3524
Classification: 20F36,  20F65,  20F67
Keywords: Artin groups, CAT(0) space, acylindrical hyperbolicity, Baum–Connes conjecture.
Haettel, Thomas 1

1 Université de Montpellier IMAG, Univ Montpellier, CNRS, France Place Eugène Bataillon 34090 Montpellier France
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Haettel, Thomas. XXL type Artin groups are CAT(0) and acylindrically hyperbolic. Annales de l'Institut Fourier, Volume 72 (2022) no. 6, pp. 2541-2555. doi : 10.5802/aif.3524. https://aif.centre-mersenne.org/articles/10.5802/aif.3524/

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