Geodesic
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.

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corrige Height, graded relative hyperbolicity and quasiconvexity
[Hauteur, hyperbolicité relative graduée, et quasiconvexité]

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.

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.

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
Mots-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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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://geodesic.mathdoc.fr/articles/10.5802/jep.97/

[DG18] Dahmani, François; Guirardel, Vincent Recognizing a relatively hyperbolic group by its Dehn fillings, Duke Math. J., Volume 167 (2018) no. 12, pp. 2189-2241 | MR | Zbl | DOI

[DM17] Dahmani, François; Mj, Mahan Height, graded relative hyperbolicity and quasiconvexity, J. Éc. polytech. Math., Volume 4 (2017), pp. 515-556 | MR | DOI

[DT17] Dowdall, Spencer; Taylor, Samuel J. The co-surface graph and the geometry of hyperbolic free group extensions, J. Topology, Volume 10 (2017) no. 2, pp. 447-482 | MR | Zbl | DOI

[DT18] Dowdall, Spencer; Taylor, Samuel J. Hyperbolic extensions of free groups, Geom. Topol., Volume 22 (2018) no. 1, pp. 517-570 | Zbl | MR | DOI

[Gro87] Gromov, M. Hyperbolic groups, Essays in group theory (Math. Sci. Res. Inst. Publ.), Volume 8, Springer, New York, 1987, pp. 75-263 | MR | Zbl | DOI

[Osi06] Osin, D. V. Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, Mem. Amer. Math. Soc., 179, no.  843, American Mathematical Society, Providence, RI, 2006 | Zbl | MR

[Raf14] Rafi, Kasra Hyperbolicity in Teichmüller space, Geom. Topol., Volume 18 (2014) no. 5, pp. 3025-3053 | Zbl | MR | DOI

[Yan12] Yang, Wen-yuan Limit sets of relatively hyperbolic groups, Geom. Dedicata, Volume 156 (2012), pp. 1-12 | Zbl | MR | DOI

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