no. 6
XXL type Artin groups are CAT(0) and acylindrically hyperbolic
[Les groupes d’Artin de type XXL sont CAT(0) et acylindriquement hyperboliques]
Haettel, Thomas1
1 Université de Montpellier IMAG, Univ Montpellier, CNRS, France Place Eugène Bataillon 34090 Montpellier France
Annales de l'Institut Fourier, Tome 72 (2022) no. 6, pp. 2541-2555.

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.

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.

Reçu le :
Révisé le :
Accepté le :
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DOI : 10.5802/aif.3524
Classification : 20F36, 20F65, 20F67
Keywords: Artin groups, CAT(0) space, acylindrical hyperbolicity, Baum–Connes conjecture.
Mot clés : Groupes d’Artin, espaces CAT(0), hyperbolicité acylindrique, conjecture de Baum–Connes.
Haettel, Thomas 1

1 Université de Montpellier IMAG, Univ Montpellier, CNRS, France Place Eugène Bataillon 34090 Montpellier France
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Haettel, Thomas. XXL type Artin groups are CAT(0) and acylindrically hyperbolic. Annales de l'Institut Fourier, Tome 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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