Constructing integrable systems of semitoric type
| dc.creator | Pelayo, Alvaro | |
| dc.creator | Ngoc, San Vu | |
| dc.date | 2009-03-19 | |
| dc.date.accessioned | 2026-07-07T12:54:17Z | |
| dc.date.available | 2026-07-07T12:54:17Z | |
| dc.description | Let M be a connected, symplectic 4-manifold. A semitoric integrable system on M essentially consists of a pair of independent, real-valued, smooth functions J and H on the manifold 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 (Invent. Math. 2009), this gives a classification of semitoric integrable systems on 4-manifolds, in terms of five invariants. Some of the invariants are geometric, others are analytic and others are combinatorial/group-theoretic. | |
| dc.description | 28 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0903.3376 | |
| dc.identifier | http://arxiv.org/abs/0903.3376 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223880 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Dynamical Systems | |
| dc.title | Constructing integrable systems of semitoric type | |
| dc.type | text |