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2011 Constructing integrable systems of semitoric type
Álvaro Pelayo, San Vũ Ngọc
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Acta Math. 206(1): 93-125 (2011). DOI: 10.1007/s11511-011-0060-4

Abstract

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.

Funding Statement

The first author was partially supported by an NSF post-doctoral fellowship. This work was done while the first author was at the Massachusetts Institute of Technology (2007–2008) and at the University of California, Berkeley (2008–2010).

Citation

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Álvaro Pelayo. San Vũ Ngọc. "Constructing integrable systems of semitoric type." Acta Math. 206 (1) 93 - 125, 2011. https://doi.org/10.1007/s11511-011-0060-4

Information

Received: 3 April 2009; Published: 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1225.53074
MathSciNet: MR2784664
Digital Object Identifier: 10.1007/s11511-011-0060-4

Rights: 2011 © Institut Mittag-Leffler

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