no. 4
Coning-off CAT(0) cube complexes
[Coller des cônes sur des complexes cubiques CAT(0)]
Genevois, Anthony1
1 University of Montpellier Institut Mathématiques Alexander Grothendieck Place Eugène Bataillon 34090 Montpellier (France)
Annales de l'Institut Fourier, Tome 71 (2021) no. 4, pp. 1535-1599.

Dans cet article, nous étudions les propriétés de courbure négative stricte d’espaces obtenus à partir de complexes cubiques CAT(0) en collant des cônes au-dessus de sous-complexes convexes. En guise d’application, nous donnons une preuve cubique directe de la caractérisation des groupes de Coxeter à angles droits relativement hyperboliques. Nous prouvons également l’hyperbolicité acylindrique des quotients à petite simplification C ′ (1/4)-T(4) des produits libres.

In this paper, we study the geometry of cone-offs of CAT(0) cube complexes over a family of combinatorially convex subcomplexes, with an emphasis on their Gromov-hyperbolicity. A first application gives a direct cubical proof of the characterization of the (strong) relative hyperbolicity of right-angled Coxeter groups, which is a particular case of a result due to Behrstock, Caprace, Hagen and Sisto. A second application gives the acylindrical hyperbolicity of C ′ (1/4)-T(4) small cancellation quotients of free products.

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DOI : 10.5802/aif.3430
Classification : 20F65, 20F67
Keywords: CAT(0) cube complexes, hyperbolicity, acylindrically hyperbolic groups, relatively hyperbolic groups, right-angled Coxeter groups, small cancellation
Mot clés : complexes cubiques, hyperbolicité, groupes acylindriquement hyperboliques, groupes relativement hyperboliques, groupes de Coxeter à angles droits, petites simplifications
Genevois, Anthony 1

1 University of Montpellier Institut Mathématiques Alexander Grothendieck Place Eugène Bataillon 34090 Montpellier (France)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Genevois, Anthony. Coning-off CAT(0) cube complexes. Annales de l'Institut Fourier, Tome 71 (2021) no. 4, pp. 1535-1599. doi : 10.5802/aif.3430. https://aif.centre-mersenne.org/articles/10.5802/aif.3430/

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