Tamed to compatible: Symplectic forms via moduli space integration

Abstract

Fix a compact 4-dimensional manifold with self-dual 2nd Betti number one and with a given symplectic form. This article proves the following: The Frechet space of tamed almost complex structures as defined by the given symplectic form has an open and dense subset whose complex structures are compatible with respect to a symplectic form that is cohomologous to the given one. The theorem is proved by constructing the new symplectic form by integrating over a space of currents that are defined by pseudo-holomorphic curves.

Minor corrections for this version

References in corpus (2)

• Taming symplectic forms and the Calabi-Yau equation
• Embedded contact homology and Seiberg-Witten Floer cohomology I

Cited by in corpus (2)

• Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
• Tamed to compatible when b^(2+) = 1 and b^1 = 2