Corrigendum to “Height graded relative hyperbolicity and quasiconvexity”
[Correction à « Hauteur, hyperbolicité relative graduée, et quasiconvexité »]
Dahmani, François1 ; Mj, Mahan2
1 Institut Fourier, Université Grenoble Alpes 100 rue des Maths, CS 40700, F-38058 Grenoble Cedex 9, France
2 Tata Institute of Fundamental Research 1, Homi Bhabha Road, Mumbai-400005, India
Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 425-432.
corrige Height, graded relative hyperbolicity and quasiconvexity
[Hauteur, hyperbolicité relative graduée, et quasiconvexité]

Une malencontreuse erreur entache la preuve, et l’énoncé, de la Proposition 5.1 de l’article mentionné en titre. Celle-ci affecte un sens d’implication du théorème principal. Nous en donnons ici une correction, qui indique que, étant donné un sous-groupe quasi-convexe d’un groupe hyperbolique, ou relativement hyperbolique, la collection des saturations des intersections multiples (et non pas des intersections multiples elles-mêmes) fournit une structure relativement hyperbolique graduée.

There is an unfortunate mistake in the statement and the proof of Proposition 5.1 of [DM17]. This affects one direction of the implications of the main theorem. A correction is given, that states that given a quasi-convex subgroup of a hyperbolic (or relatively hyperbolic) group, the graded relative hyperbolic structure holds with respect to saturations of i-fold intersections, that are stabilizers of limit sets of i-fold intersections.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.97
Classification : 20F65, 20F67, 22E40
Keywords: Quasi-convex subgroups, hyperbolic groups, relatively hyperbolic groups, convex cocompact groups
Mot clés : Sous-groupes quasi-convexes, groupes hyperboliques, groupes relativement hyperboliques, groupes convexes cocompacts
Dahmani, François 1 ; Mj, Mahan 2

1 Institut Fourier, Université Grenoble Alpes 100 rue des Maths, CS 40700, F-38058 Grenoble Cedex 9, France
2 Tata Institute of Fundamental Research 1, Homi Bhabha Road, Mumbai-400005, India 
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Dahmani, François; Mj, Mahan. Corrigendum to  “Height graded relative hyperbolicity and quasiconvexity”. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 425-432. doi : 10.5802/jep.97. http://www.numdam.org/articles/10.5802/jep.97/

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