Continuity of the bending map

Cyril Lecuire[1]

  • [1] Laboratoire Emile Picard, Université Paul Sabatier 118 route de Narbonne, 31062 Toulouse Cedex 9

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 1, page 93-119
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Lecuire, Cyril. "Continuity of the bending map." Annales de la faculté des sciences de Toulouse Mathématiques 17.1 (2008): 93-119. <http://eudml.org/doc/10084>.

@article{Lecuire2008,
abstract = {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.},
affiliation = {Laboratoire Emile Picard, Université Paul Sabatier 118 route de Narbonne, 31062 Toulouse Cedex 9},
author = {Lecuire, Cyril},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {hyperbolic manifold; bending map; core; geodesic lamination; complete hyperbolic metric; convex compact},
language = {eng},
month = {6},
number = {1},
pages = {93-119},
publisher = {Université Paul Sabatier, Toulouse},
title = {Continuity of the bending map},
url = {http://eudml.org/doc/10084},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Lecuire, Cyril
TI - Continuity of the bending map
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 1
SP - 93
EP - 119
AB - 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.
LA - eng
KW - hyperbolic manifold; bending map; core; geodesic lamination; complete hyperbolic metric; convex compact
UR - http://eudml.org/doc/10084
ER -

References

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