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June 2010 Almost toric symplectic four-manifolds
Naichung Conan Leung, Margaret Symington
J. Symplectic Geom. 8(2): 143-187 (June 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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Naichung Conan Leung. Margaret Symington. "Almost toric symplectic four-manifolds." J. Symplectic Geom. 8 (2) 143 - 187, June 2010.


Published: June 2010
First available in Project Euclid: 15 July 2010

zbMATH: 1197.53103
MathSciNet: MR2670163

Rights: Copyright © 2010 International Press of Boston


Vol.8 • No. 2 • June 2010
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