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| HAL: hal-00605417, version 1 |
| arXiv: 0903.3376 |
| DOI: 10.1007/s11511-011-0060-4 |
| Detailed view |  Export this paper |
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| Acta Mathematica 206, 1 (2011) 93-125 |
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| Constructing integrable systems of semitoric type |
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| Alvaro Pelayo 1San Vu Ngoc 2 |
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| (2011) |
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| Let M be a connected, symplectic 4-manifold. A semitoric integrable system on M essentially consists of a pair of independent, real-valued, smooth functions J and H on the manifold M, for which J generates a Hamiltonian circle action under which H is invariant. In this paper we give a general method to construct, starting from a collection of five ingredients, a symplectic 4-manifold equipped a semitoric integrable system. Then we show that every semitoric integrable system on a symplectic 4-manifold is obtained in this fashion. In conjunction with the uniqueness theorem proved recently by the authors (Invent. Math. 2009), this gives a classification of semitoric integrable systems on 4-manifolds, in terms of five invariants. Some of the invariants are geometric, others are analytic and others are combinatorial/group-theoretic. |
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| 1: | Mathematics Department |
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University of California, Berkeley |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Equations aux dérivées partielles |
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| Subject | : | Mathematics/Symplectic Geometry Mathematics/Dynamical Systems |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/0903.3376 |
| hal-00605417, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00605417 | |
| oai:hal.archives-ouvertes.fr:hal-00605417 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Friday, 1 July 2011 14:31:39 | |
| Updated on: Wednesday, 13 June 2012 11:30:48 | |
