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The Seiberg-Witten invariants of symplectic four-manifolds (after C. H. Taubes). (English) Zbl 0882.57026

Séminaire Bourbaki. Volume 1995/96. Exposés 805–819. Paris: Société Mathématique de France, Astérisque. 241, 195-220, Exp. No. 812 (1997).
The author gives a survey of Seiberg-Witten invariants and describes results of C. H. Taubes [Math. Res. Lett. 2, No. 2, 221-238 (1995; Zbl 0854.57020); “From the Seiberg-Witten equation to pseudo holomorphic curves” J. Am. Math. Soc. 9, No. 3, 845-918 (1996; Zbl 0867.53025)]. He then discusses applications of Taubes’s theorems about the equivalence of the Seiberg-Witten invariants. For example, he points out that the symplectic structure of \(\mathbb{C} P^2\) is unique and he shows that many minimal symplectic four-manifolds do not admit any nontrivial connected sum decompositions.
For the entire collection see [Zbl 0866.00026].

MSC:

57R57 Applications of global analysis to structures on manifolds
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
58D27 Moduli problems for differential geometric structures
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