Almost toric symplectic four-manifolds

2003/12/08 by Naichung Conan Leung, Leung, Naichung Conan, Margaret Symington +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.GT #math.SG #msc:53D05

paper · pdf · doi:10.48550/arxiv.math/0312165

36 pages, 9 figures

arxiv created 2003/12/08 · arxiv updated 2009/12/01

Abstract

Almost toric manifolds form a class of singular Lagrangian fibered symplectic manifolds that is a natural generalization of toric manifolds. Notable examples include the K3 surface, the phase space of the spherical pendulum and rational balls useful for symplectic surgeries. The main result of the paper is a complete classification up to diffeomorphism of closed almost toric four-manifolds. A key step in the proof is a geometric classification of the singular affine structures that can occur on the base of a closed almost toric four-manifold.

Citations

• On global action‐angle coordinates

Cited by

• Almost toric fibrations on symplectic blow ups

Related

• Toric structures on near-symplectic 4-manifolds
• A note on the symplectic classification of almost-toric systems
• Pseudo symplectic geometry as an extension of the symplectic geometry
• Delzant-type classification of near-symplectic toric 4-manifolds
• Constructions of small symplectic 4-manifolds using Luttinger surgery