Coning-off CAT(0) cube complexes
[Coller des cônes sur des complexes cubiques CAT(0)]
Annales de l'Institut Fourier, Online first, 65 p.

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 : https://doi.org/10.5802/aif.3430
Classification : 20F65,  20F67
Mots clés : complexes cubiques, hyperbolicité, groupes acylindriquement hyperboliques, groupes relativement hyperboliques, groupes de Coxeter à angles droits, petites simplifications
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Genevois, Anthony. Coning-off CAT(0) cube complexes. Annales de l'Institut Fourier, Online first, 65 p.

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