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Continuity of the bending map
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 1, pp. 93-119.

The bending map of a hyperbolic 3-manifold maps a convex cocompact hyperbolic metric on a 3-manifold with boundary to its bending measured geodesic lamination. As proved in [KeS] and [KaT], this map is continuous. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the space of measured geodesic laminations and show that the quotient map obtained from the bending map is continuous.

L’application de plissage d’une variété hyperbolique de dimension 3 associe à une métrique hyperbolique convexe cocompacte sur une variété compacte à bord sa lamination géodésique mesurée de plissage. Il a été démontré dans [KeS] et [KaT] que cette application est continue. Dans ce texte, on étudie l’extension de cette application à l’espace des métriques hyperboliques géométriquement finies. On introduit une relation d’équivalence dans l’espace des laminations géodésiques mesurées et on montre que l’application quotient de l’application de plissage est continue.

DOI: 10.5802/afst.1178
Cyril Lecuire 1

1 Laboratoire Emile Picard, Université Paul Sabatier 118 route de Narbonne, 31062 Toulouse Cedex 9
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     author = {Cyril Lecuire},
     title = {Continuity of the bending map},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {93--119},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 17},
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Cyril Lecuire. Continuity of the bending map. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 1, pp. 93-119. doi : 10.5802/afst.1178. https://afst.centre-mersenne.org/articles/10.5802/afst.1178/

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