Thurston’s compactification via geodesic currents: the case of non-compact finite area surfaces
[Compactification de Thurston par les courants géodésiques : le cas des surfaces non-compactes d’aire finie]
Trin, Marie1
1 Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes (France)
Annales de l'Institut Fourier, Online first, 22 p.

En 1988, Bonahon a donné une preuve de la compactification de Thurston de l’espace de Teichmüller utilisant les courants géodésiques. Pour des raisons bien précises, cette preuve ne s’applique que dans le cas des surfaces fermées. On présente ici une variante des arguments de Bonahon qui s’applique aux surfaces d’aire finie grâce à un théorème de contrôle sur les suites de géodésiques aléatoires. Notons que ce théorème a son propre intérêt notamment lorsque la surface n’est pas compacte.

In 1988, Bonahon gave a construction of Thurston’s compactification of Teichmüller space using geodesic currents. His argument only applies in the case of closed surfaces, and there are good reasons for that. We present a variant which applies to surfaces of finite area and to do so we prove a control theorem for sequences of random geodesics. Note that this theorem may be of independant interest, especially when the surface is non-compact.

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DOI : 10.5802/aif.3625
Classification : 57K20, 53C22, 57M50, 37D40
Keywords: Teichmüller space, Thurston’s compactification, Geodesic currents, Sequences of random geodesics.
Mot clés : Espace de Teichmüller, compactification de Thurston, courants géodésiques, suites de géodésiques aléatoires.
Trin, Marie 1

1 Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes (France) 
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Trin, Marie. Thurston’s compactification via geodesic currents: the case of non-compact finite area surfaces. Annales de l'Institut Fourier, Online first, 22 p.

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