Journal of Symplectic Geometry

Volume 8 (2010)

Number 2

Fold-forms for four-folds

Pages: 189 – 203

DOI: http://dx.doi.org/10.4310/JSG.2010.v8.n2.a3

Author

Ana Cannas da Silva

Abstract

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.

Full Text (PDF format)