## Journal of Symplectic Geometry

### Tamed to compatible: symplectic forms via moduli space integration

Clifford Henry Taubes

#### Abstract

Fix a compact 4-dimensional manifold with self-dual second Betti number one and with a given symplectic form. This article proves the following: The Frêchet 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.

#### Article information

Source
J. Symplectic Geom. Volume 9, Number 2 (2011), 161-250.

Dates
First available in Project Euclid: 1 July 2011