Semitoric integrable systems on symplectic 4-manifolds

Details Semitoric integrable systems on symplectic 4-manifolds Semitoric integrable systems on symplectic 4-manifolds

2008-06-11

arxiv.org/abs/0806.1946v1

Mathematics

Symplectic Geometry

Scientific paper

Let M be a symplectic 4-manifold. A semitoric integrable system on M is a pair of real-valued smooth functions J, H on M 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.

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