Semitoric integrable systems on symplectic 4-manifolds

• 成果类型: Article
• 署名作者: Pelayo, Alvaro; Ngoc, San Vu
• 署名单位: University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT); Universite de Rennes
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0190-x
• 发表日期: 2009
• 页码: 571-597
• 关键词: convexity properties; hamiltonian-systems; torus actions

摘要

Let (M, omega) be a symplectic 4-manifold. A semitoric integrable system on (M, omega) is a pair of smooth functions J, H is an element of C-infinity( M, R) 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.