Configurations de connexions de selles et échanges d'intervalles généralisés dans l'espace des modules des différentielles quadratiques

Abstract : We are interested in rigid families of saddle connections on half-translation surfaces. Studying the corresponding configurations is a first step to understand the geometry at infinity of the strata of the moduli space of quadratic differentials. We extend a result of Masur and Zorich by classifying the configurations for each connected components of each stratum when the genus is greater than or equal to five. Then we perform a finer study of some specific degenerations and prove in particular that a stratum has only one topological end when the genus is zero.

The relation between translation surfaces and interval exchanges provides a powerfull tool to analyse the corresponding Teichmüller flow. We generalize this relation to the case of quadratic differentials. We relate the geomery and dynamics of such maps to explicit combinatorial criteria for the corresponding generalized permutations.
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Theses
Mathematics [math]. Université Rennes 1, 2007. French


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Contributor : Corentin Boissy <>
Submitted on : Thursday, February 28, 2008 - 5:10:01 PM
Last modification on : Friday, March 27, 2015 - 9:59:46 AM

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Corentin Boissy. Configurations de connexions de selles et échanges d'intervalles généralisés dans l'espace des modules des différentielles quadratiques. Mathematics [math]. Université Rennes 1, 2007. French. <tel-00259639>

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