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June 2011 Tamed to compatible: symplectic forms via moduli space integration
Clifford Henry Taubes
J. Symplectic Geom. 9(2): 161-250 (June 2011).


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.


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Clifford Henry Taubes. "Tamed to compatible: symplectic forms via moduli space integration." J. Symplectic Geom. 9 (2) 161 - 250, June 2011.


Published: June 2011
First available in Project Euclid: 1 July 2011

zbMATH: 1232.57021
MathSciNet: MR2811651

Rights: Copyright © 2011 International Press of Boston


Vol.9 • No. 2 • June 2011
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