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June 2010 Fold-forms for four-folds
Ana Cannas da Silva
J. Symplectic Geom. 8(2): 189-203 (June 2010).


This paper explains an application of Gromov’s h-principle to prove the existence, on any orientable four-manifold, of a folded symplectic form. That is a closed two-form which is symplectic except on a separating hypersurface where the form singularities are like the pullback of a symplectic form by a folding map. We use the h-principle for folding maps (a theorem of Eliashberg) and the h-principle for symplectic forms on open manifolds (a theorem of Gromov) to show that, for orientable even-dimensional manifolds, the existence of a stable almost complex structure is necessary and sufficient to warrant the existence of a folded symplectic form.


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Ana Cannas da Silva. "Fold-forms for four-folds." J. Symplectic Geom. 8 (2) 189 - 203, June 2010.


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

zbMATH: 1200.53078
MathSciNet: MR2670164

Rights: Copyright © 2010 International Press of Boston


Vol.8 • No. 2 • June 2010
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