# THE SEIBERG-WITTEN INVARIANTS AND SYMPLECTIC FORMS

@article{Taubes1994THESI, title={THE SEIBERG-WITTEN INVARIANTS AND SYMPLECTIC FORMS}, author={C. Taubes}, journal={Mathematical Research Letters}, year={1994}, volume={1}, pages={809-822} }

(Note: There are no symplectic forms on X unless b and the first Betti number of X have opposite parity.) In a subsequent article with joint authors, a vanishing theorem will be proved for the Seiberg-Witten invariants of a manifold X, as in the theorem, which can be split by an embedded 3-sphere as X−∪X+ where neither X− nor X+ have negative definite intersection forms. Thus, no such manifold admits a symplectic form. That is,

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