Journal of Symplectic Geometry

Almost toric symplectic four-manifolds

Naichung Conan Leung and Margaret Symington

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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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J. Symplectic Geom., Volume 8, Number 2 (2010), 143-187.

First available in Project Euclid: 15 July 2010

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Leung, Naichung Conan; Symington, Margaret. Almost toric symplectic four-manifolds. J. Symplectic Geom. 8 (2010), no. 2, 143--187.

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