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| HAL : hal-00188546, version 1 |
| DOI : 10.1017/S0305004107000023 |
| Fiche détaillée |  Récupérer au format |
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| Mathematical Proceedings of the Cambridge Philosophical Society 142, 3 (2007) 487-496 |
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| On the topology defined by Thurston's asymmetric metric |
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| Athanase Papadopoulos 1Guillaume Théret 2 |
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| (2007) |
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| In this paper, we establish some properties of Thurston's asymmetric metric L on the Teichmueller space T of a surface with negative Euler characteristic. We study convergence of sequences of elements in T in the sense of L, as well as sequences that tend to infinity in T. We show that the topology that the asymmetric metric induces on Teichmueller space is the same as the usual topology. Furthermore, we show that L satisfies the axioms of a (not necessarily symmetric) metric in the sense of Busemann and conclude that L is complete in the sense of Busemann. |
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| 1 : | Institut de Recherche Mathématique Avancée (IRMA) |
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CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I |
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| 2 : | Center for the topology and quantization of moduli spaces (CTQM) |
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Aarhus Universitat |
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| Domaine | : | Mathématiques/Topologie géométrique |
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| Teichmueller space – Thurston's asymmetric metric – weak metric – Busemann – geodesic lamination |
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| hal-00188546, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00188546 | |
| oai:hal.archives-ouvertes.fr:hal-00188546 | |
| Contributeur : Athanase Papadopoulos | |
| Soumis le : Dimanche 18 Novembre 2007, 04:57:25 | |
| Dernière modification le : Dimanche 18 Novembre 2007, 05:46:20 | |
