We prove that infinitely presented graphical small cancellation groups are acylindrically hyperbolic. In particular, infinitely presented classical -groups and, hence, classical -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 -groups that provide new examples of divergence functions of groups.
Nous démontrons que les groupes de présentation infinie satisfaisant la condition de petite simplification graphique sont acylindriquement hyperboliques. Cette classe contient les groupes satisfaisant la condition classique de petite simplification graphique et par conséquent ceux vérifiant la condition . 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 qui fournissent de nouveaux exemples de fonctions de divergence des groupes.
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Keywords: Graphical small cancellation, acylindrical hyperbolicity, divergence
Mot clés : Petite simplification graphique, hyperbolicité acylindrique, divergence
Gruber, Dominik 1; Sisto, Alessandro 1
@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{\textquoteright}institut Fourier}, volume = {68}, number = {6}, year = {2018}, doi = {10.5802/aif.3215}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3215/} }
TY - JOUR AU - Gruber, Dominik AU - Sisto, Alessandro TI - Infinitely presented graphical small cancellation groups are acylindrically hyperbolic JO - Annales de l'Institut Fourier PY - 2018 SP - 2501 EP - 2552 VL - 68 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3215/ DO - 10.5802/aif.3215 LA - en ID - AIF_2018__68_6_2501_0 ER -
%0 Journal Article %A Gruber, Dominik %A Sisto, Alessandro %T Infinitely presented graphical small cancellation groups are acylindrically hyperbolic %J Annales de l'Institut Fourier %D 2018 %P 2501-2552 %V 68 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3215/ %R 10.5802/aif.3215 %G en %F AIF_2018__68_6_2501_0
Gruber, Dominik; Sisto, Alessandro. Infinitely presented graphical small cancellation groups are acylindrically hyperbolic. Annales de l'Institut Fourier, Volume 68 (2018) no. 6, pp. 2501-2552. doi : 10.5802/aif.3215. https://aif.centre-mersenne.org/articles/10.5802/aif.3215/
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