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François Dahmani; Mahan Mj
Height, graded relative hyperbolicity and quasiconvexity
(Hauteur, hyperbolicité relative graduée, et quasiconvexité)
Journal de l'École polytechnique — Mathématiques, 4 (2017), p. 515-556, doi: 10.5802/jep.50
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Class. Math.: 20F65, 20F67, 22E40
Mots clés: Sous-groupes quasi-convexes, groupes hyperboliques, groupes relativement hyperboliques, groupes convexes cocompacts

Résumé - Abstract

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.

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