- Acta Math.
- Volume 206, Number 1 (2011), 93-125.
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.
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).
Acta Math., Volume 206, Number 1 (2011), 93-125.
Received: 3 April 2009
First available in Project Euclid: 31 January 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
2011 © Institut Mittag-Leffler
Pelayo, Álvaro; Vũ Ngọc, San. Constructing integrable systems of semitoric type. Acta Math. 206 (2011), no. 1, 93--125. doi:10.1007/s11511-011-0060-4. https://projecteuclid.org/euclid.acta/1485892529