We describe a simple locally CAT(0) classifying space for XXL type Artin groups (with all labels at least ). Furthermore, when the Artin group is not dihedral, we describe a rank 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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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
@article{AIF_2022__72_6_2541_0, author = {Haettel, Thomas}, title = {XXL type {Artin} groups are {CAT(0)} and acylindrically hyperbolic}, journal = {Annales de l'Institut Fourier}, pages = {2541--2555}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {72}, number = {6}, year = {2022}, doi = {10.5802/aif.3524}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3524/} }
TY - JOUR AU - Haettel, Thomas TI - XXL type Artin groups are CAT(0) and acylindrically hyperbolic JO - Annales de l'Institut Fourier PY - 2022 SP - 2541 EP - 2555 VL - 72 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3524/ DO - 10.5802/aif.3524 LA - en ID - AIF_2022__72_6_2541_0 ER -
%0 Journal Article %A Haettel, Thomas %T XXL type Artin groups are CAT(0) and acylindrically hyperbolic %J Annales de l'Institut Fourier %D 2022 %P 2541-2555 %V 72 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3524/ %R 10.5802/aif.3524 %G en %F AIF_2022__72_6_2541_0
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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