Almost toric symplectic four-manifolds

Conan Leung Chinese Univ of HK Margaret Symington

Symplectic Geometry mathscidoc:1608.34013

Journal of Symplectic Geometry, 8, (2), 143-187, 2010
Almost toric manifolds form a class of singular Lagrangian fibered symplectic manifolds that include both toric manifolds and the K3 surface. We classify closed almost toric four-manifolds up to diffeomorphism and indicate precisely the structure of all almost toric fibrations of closed symplectic four-manifolds. A key step in the proof is a geometric classification of the singular integral affine structures that can occur on the base of an almost toric fibration of a closed four-manifold. As a byproduct we provide a geometric explanation for why a generic Lagrangian fibration over the two-sphere must have 24 singular fibers.
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  title={Almost toric symplectic four-manifolds},
  author={Conan Leung, and Margaret Symington},
  booktitle={Journal of Symplectic Geometry},
Conan Leung, and Margaret Symington. Almost toric symplectic four-manifolds. 2010. Vol. 8. In Journal of Symplectic Geometry. pp.143-187.
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