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Inventiones mathematicae

, Volume 94, Issue 1, pp 53–80 | Cite as

Topologie de Gromov équivariante, structures hyperboliques et arbres réels

  • Frédéric Paulin
Article

Résumé

Les objets que nous étudions sont les espaces métriques munis d'une action par isométrie d'un groupe fixé Γ. Nous définissons une «topologie» naturelle sur «l'ensemble» de ces espaces. Nous montrons un critère de compacité séquentielle par des méthodes inspirées des travaux de M. Gromov. Nous utilisons ce critère pour donner une preuve plus courte et plus géométrique de deux théorèmes: celui de M. Culler et J. Morgan sur la compacité de l'espace des arbres réels à petits stabilisateurs d'arêtes; et celui de J. Morgan sur la compactification de l'espace des structures hyperboliques sur une variété par des arbres réels à petits stabilisateurs d'arêtes.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Frédéric Paulin
    • 1
  1. 1.Université Paris XIOrsay CedexFrance

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