Height, graded relative hyperbolicity and quasiconvexity
[Hauteur, hyperbolicité relative graduée, et quasiconvexité]
Journal de l’École polytechnique — Mathématiques, Tome 4 (2017), pp. 515-556.

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 Out(F n ).

Reçu le :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/jep.50
Classification : 20F65,  20F67,  22E40
Mots clés : Sous-groupes quasi-convexes, groupes hyperboliques, groupes relativement hyperboliques, groupes convexes cocompacts
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     author = {Dahmani, Fran\c{c}ois and Mj, Mahan},
     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 = {http://www.numdam.org/articles/10.5802/jep.50/}
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Dahmani, François; Mj, Mahan. Height, graded relative hyperbolicity and quasiconvexity. Journal de l’École polytechnique — Mathématiques, Tome 4 (2017), pp. 515-556. doi : 10.5802/jep.50. http://www.numdam.org/articles/10.5802/jep.50/

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