Infinitely presented graphical small cancellation groups are acylindrically hyperbolic  [ Les groupes à petite simplification graphique de présentation infinie sont acylindriquement hyperboliques ]
Annales de l'Institut Fourier, Tome 68 (2018) no. 6, pp. 2501-2552.

Nous démontrons que les groupes de présentation infinie satisfaisant la condition de petite simplification graphique Gr(7) sont acylindriquement hyperboliques. Cette classe contient les groupes satisfaisant la condition classique de petite simplification graphique C(7) et par conséquent ceux vérifiant la condition C ' (1 6). Plus généralement, nous démontrons des énoncés analogues valables pour les presentations à petite simplification graphique dans un produit libre. Nous construisons des présentations infinies vérifiant la conditions classique C ' (1 6) qui fournissent de nouveaux exemples de fonctions de divergence des groupes.

We prove that infinitely presented graphical Gr(7) small cancellation groups are acylindrically hyperbolic. In particular, infinitely presented classical C(7)-groups and, hence, classical C ' (1 6)-groups are acylindrically hyperbolic. We also prove the analogous statements for the larger class of graphical small cancellation presentations over free products. We construct infinitely presented classical C ' (1 6)-groups that provide new examples of divergence functions of groups.

Reçu le : 2017-06-19
Accepté le : 2017-11-07
Publié le : 2018-11-23
DOI : https://doi.org/10.5802/aif.3215
Classification : 20F06,  20F65,  20F67
Mots clés: Petite simplification graphique, hyperbolicité acylindrique, divergence
@article{AIF_2018__68_6_2501_0,
     author = {Gruber, Dominik and Sisto, Alessandro},
     title = {Infinitely presented graphical small cancellation groups are acylindrically hyperbolic},
     journal = {Annales de l'Institut Fourier},
     pages = {2501--2552},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {6},
     year = {2018},
     doi = {10.5802/aif.3215},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2018__68_6_2501_0/}
}
Gruber, Dominik; Sisto, Alessandro. Infinitely presented graphical small cancellation groups are acylindrically hyperbolic. Annales de l'Institut Fourier, Tome 68 (2018) no. 6, pp. 2501-2552. doi : 10.5802/aif.3215. https://aif.centre-mersenne.org/item/AIF_2018__68_6_2501_0/

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