Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials
| Autor: | Anton Zorich |
|---|---|
| Přispěvatelé: | Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Collin, Maryse, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) |
| Rok vydání: | 2010 |
| Předmět: |
Rauzy class
Jenkins-Strebel differential Pure mathematics Interval exchange transformation Geodesic Dynamical Systems (math.DS) Permutation Mathematics - Geometric Topology Mathematics - Algebraic Geometry Quadratic equation FOS: Mathematics Abelian group Mathematics - Dynamical Systems 32G15 30F30 30F60 37E05 37E35 37G99 Algebraic Geometry (math.AG) ComputingMilieux_MISCELLANEOUS Teichmuller geodesic flow Mathematics Connected component Algebra and Number Theory Applied Mathematics Geometric Topology (math.GT) spin structure Moduli space Component (group theory) interval-exchange transformation moduli space of quadratic differentials Analysis |
| Zdroj: | Journal of modern dynamics Journal of modern dynamics, American Institute of Mathematical Sciences, 2008, 2 (1), pp.139-185 Journal of modern dynamics, 2008, 2 (1), pp.139-185 |
| ISSN: | 1930-5311 1930-532X |
| DOI: | 10.48550/arxiv.1011.0395 |
| Popis: | Moduli spaces of Abelian and quadratic differentials are stratified by multiplicities of zeroes; connected components of the strata correspond to ergodic components of the Teichmuller geodesic flow. It is known that the strata are not necessarily connected; the connected components were recently classified by M. Kontsevich and the author and by E. Lanneau. The strata can be also viewed as families of flat metrics with conical singularities and with Z/2Z-holonomy. For every connected component of each stratum of Abelian and quadratic differentials we construct an explicit representative which is a Jenkins-Strebel differential with a single cylinder. By an elementary variation of this construction we represent almost every Abelian (quadratic) differential in the corresponding connected component of the stratum as a polygon with identified pairs of edges, where combinatorics of identifications is explicitly described. Specifically, the combinatorics is expressed in terms of a generalized permutation. For any component of any stratum of Abelian and quadratic differentials we construct a generalized permutation (linear involution) in the corresponding extended Rauzy class. Comment: 47 pages |
| Databáze: | OpenAIRE |
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