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Inventiones mathematicae

, Volume 177, Issue 3, pp 571–597 | Cite as

Semitoric integrable systems on symplectic 4-manifolds

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Abstract

Let (M,ω) be a symplectic 4-manifold. A semitoric integrable system on (M,ω) is a pair of smooth functions J,H∈C ∞(M,ℝ) for which J generates a Hamiltonian S 1-action and the Poisson brackets {J,H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about the singularities and how they stand with respect to the system. Our goal is to prove that a semitoric system is completely determined by the invariants we introduce.

Keywords

Local Diffeomorphism Singular Foliation Symplectic Invariant Elliptic Singularity Equivariant Normal Form 
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© The Author(s) 2009

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of California–BerkeleyBerkeleyUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA
  3. 3.Institut de Recherches Mathématiques de RennesUniversité de Rennes 1Rennes cedexFrance

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