Tamed to compatible: Symplectic forms via moduli space integration

Details Tamed to compatible: Symplectic forms via moduli space integration Tamed to compatible: Symplectic forms via moduli space integration

2009-10-28

arxiv.org/abs/0910.5440v1

Mathematics

Symplectic Geometry

Scientific paper

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.

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