Acta Mathematica

, 206:93 | Cite as

Constructing integrable systems of semitoric type



Let (M, ω) be a connected, symplectic 4-manifold. A semitoric integrable system on (M, ω) essentially consists of a pair of independent, real-valued, smooth functions J and H on 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, this gives a classification of semitoric integrable systems on 4-manifolds, in terms of five invariants.


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Copyright information

© Institut Mittag-Leffler 2011

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonU.S.A.
  2. 2.Washington University in St. Louis, Department of MathematicsSt. LouisU.S.A.
  3. 3.Institut de Recherches Mathématiques de Rennes, Université de Rennes 1Rennes cedexFrance

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