[Correction à « 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 -fold intersections, that are stabilizers of limit sets of -fold intersections.
Accepté le :
Publié le :
DOI : 10.5802/jep.97
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
François Dahmani 1 ; Mahan Mj 2
CC-BY 4.0
@article{JEP_2019__6__425_0,
author = {Fran\c{c}ois Dahmani and Mahan Mj},
title = {Corrigendum to {{\textquotedblleft}Height} graded relative hyperbolicity and quasiconvexity{\textquotedblright}},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {425--432},
publisher = {\'Ecole polytechnique},
volume = {6},
year = {2019},
doi = {10.5802/jep.97},
zbl = {07070265},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.97/}
}
TY - JOUR AU - François Dahmani AU - Mahan Mj TI - Corrigendum to “Height graded relative hyperbolicity and quasiconvexity” JO - Journal de l’École polytechnique — Mathématiques PY - 2019 SP - 425 EP - 432 VL - 6 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.97/ DO - 10.5802/jep.97 LA - en ID - JEP_2019__6__425_0 ER -
%0 Journal Article %A François Dahmani %A Mahan Mj %T Corrigendum to “Height graded relative hyperbolicity and quasiconvexity” %J Journal de l’École polytechnique — Mathématiques %D 2019 %P 425-432 %V 6 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.97/ %R 10.5802/jep.97 %G en %F JEP_2019__6__425_0
François Dahmani; Mahan Mj. 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. https://jep.centre-mersenne.org/articles/10.5802/jep.97/
[DG18] - “Recognizing a relatively hyperbolic group by its Dehn fillings”, Duke Math. J. 167 (2018) no. 12, p. 2189-2241 | DOI | MR | Zbl
[DM17] - “Height, graded relative hyperbolicity and quasiconvexity”, J. Éc. polytech. Math. 4 (2017), p. 515-556 | DOI | MR | Zbl
[DT17] - “The co-surface graph and the geometry of hyperbolic free group extensions”, J. Topology 10 (2017) no. 2, p. 447-482 | DOI | MR | Zbl
[DT18] - “Hyperbolic extensions of free groups”, Geom. Topol. 22 (2018) no. 1, p. 517-570 | DOI | MR | Zbl
[Gro87] - “Hyperbolic groups”, in Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, p. 75-263 | DOI | MR | Zbl
[Osi06] - Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, Mem. Amer. Math. Soc., vol. 179, no. 843, American Mathematical Society, Providence, RI, 2006 | MR | Zbl
[Raf14] - “Hyperbolicity in Teichmüller space”, Geom. Topol. 18 (2014) no. 5, p. 3025-3053 | DOI | MR | Zbl
[Yan12] - “Limit sets of relatively hyperbolic groups”, Geom. Dedicata 156 (2012), p. 1-12 | DOI | MR | Zbl
Cité par Sources :