Constructing integrable systems of semitoric type

By 'Alvaro Pelayo, San Vũ Ngọc. 2009

91 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bab48d68d5e475dbf26d5d4e4631dd590bdd51d8

How researchers see this paper

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In Geometry and Topology

1. S. Tolman
2. 'Alvaro Pelayo
3. Christopher Woodward

In Mathematical Physics

1. S. Tolman
2. 'Alvaro Pelayo
3. Christopher Woodward

Citations in the corpus

• Fixed points of symplectic periodic flows (2010, background): “diagrams in the modern global theory of integrable systems, see [17], [13], [ 14 ].”
• Symplectic theory of completely integrable Hamiltonian systems (2011, unknown): “The details of how to do this have appeared in [88].”