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| HAL : hal-00718704, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Communications in Analysis and Geometry 20, 2 (2012) p. 369-395 |
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| The behaviour of Fenchel-Nielsen distance under a change of pants decomposition |
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| Athanase Papadopoulos 1Lixin Liu 2 |
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| (2012) |
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| Given a topological orientable surface S of finite or infinite type equipped with a pair of pants decomposition P and given a base complex structure X on S, there is an associated deformation space of complex structures on S, which we call the Fenchel-Nielsen Teichmülller space associated to the pair (P,X). This space carries a metric, which we call the Fenchel-Nielsen metric, defined using Fenchel-Nielsen coordinates. We studied this metric in previous papers, and we compared it with the classical Teichmüller metric (defined using quasi-conformal mappings) and to the length spectrum metric (defined using ratios of hyperbolic lengths of simple closed curves). In the present paper, we show that under a change of pair of pants decomposition, the identity map between the corresponding Fenchel-Nielsen metrics is not necessarily bi- Lipschitz. These results complement results obtained in the previous papers and they show that these previous results are optimal. |
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| 1 : | Institut de Recherche Mathématique Avancée (IRMA) |
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CNRS : UMR7501 – Université de Strasbourg |
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| 2 : | Department of Mathematics |
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Zhongshan University |
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| 3 : | Département de Mathématiques, Université de Fribourg |
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Département de Mathématiques, Université de Fribourg |
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| 4 : | Fudan University |
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Fudan University |
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| Domaine | : | Mathématiques/Topologie géométrique |
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| Teichmüller space – Fenchel-Nielsen coordinates – Fenchel-Nielsen metric |
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| hal-00718704, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00718704 | |
| oai:hal.archives-ouvertes.fr:hal-00718704 | |
| Contributeur : Athanase Papadopoulos | |
| Soumis le : Mercredi 18 Juillet 2012, 07:15:37 | |
| Dernière modification le : Mercredi 18 Juillet 2012, 07:15:37 | |
