[Hauteur, hyperbolicité relative graduée, et quasiconvexité]
Nous introduisons les notions de hauteur géométrique d’un sous-groupe, et d’hyperbolicité relative graduée d’un groupe, avec une version géométrique de cette dernière. Nous utilisons ensuite ces notions pour caractériser la quasiconvexité des sous-groupes des groupes hyperboliques, la quasiconvexité relative des sous-groupes des groupes relativement hyperboliques, et le fait d’être convexe-cocompact dans un groupe modulaire de surface, ou dans un groupe d’automorphismes extérieurs de groupe libre.
We introduce the notions of geometric height and graded (geometric) relative hyperbolicity in this paper. We use these to characterize quasiconvexity in hyperbolic groups, relative quasiconvexity in relatively hyperbolic groups, and convex cocompactness in mapping class groups and .
Accepté le :
Publié le :
DOI : 10.5802/jep.50
Keywords: Quasiconvex subgroups, hyperbolic groups, relatively hyperbolic groups, height, convex cocompact subgroups
Mot clés : Sous-groupes quasi-convexes, groupes hyperboliques, groupes relativement hyperboliques, groupes convexes cocompacts
François Dahmani 1 ; Mahan Mj 2
CC-BY-ND 4.0
@article{JEP_2017__4__515_0,
author = {Fran\c{c}ois Dahmani and Mahan Mj},
title = {Height, graded relative hyperbolicity and quasiconvexity},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {515--556},
publisher = {\'Ecole polytechnique},
volume = {4},
year = {2017},
doi = {10.5802/jep.50},
zbl = {06754335},
mrnumber = {3646028},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.50/}
}
TY - JOUR AU - François Dahmani AU - Mahan Mj TI - Height, graded relative hyperbolicity and quasiconvexity JO - Journal de l’École polytechnique — Mathématiques PY - 2017 SP - 515 EP - 556 VL - 4 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.50/ DO - 10.5802/jep.50 LA - en ID - JEP_2017__4__515_0 ER -
%0 Journal Article %A François Dahmani %A Mahan Mj %T Height, graded relative hyperbolicity and quasiconvexity %J Journal de l’École polytechnique — Mathématiques %D 2017 %P 515-556 %V 4 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.50/ %R 10.5802/jep.50 %G en %F JEP_2017__4__515_0
François Dahmani; Mahan Mj. Height, graded relative hyperbolicity and quasiconvexity. Journal de l’École polytechnique — Mathématiques, Tome 4 (2017), pp. 515-556. doi : 10.5802/jep.50. https://jep.centre-mersenne.org/articles/10.5802/jep.50/
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