Journal of Symplectic Geometry

Tamed to compatible: symplectic forms via moduli space integration

Clifford Henry Taubes

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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

Permanent link to this document
http://projecteuclid.org/euclid.jsg/1309546043

Mathematical Reviews number (MathSciNet)
MR2811651

Zentralblatt MATH identifier
05956535

Citation

Taubes, Clifford Henry. Tamed to compatible: symplectic forms via moduli space integration. J. Symplectic Geom. 9 (2011), no. 2, 161--250. http://projecteuclid.org/euclid.jsg/1309546043.


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