ArticleOriginal scientific text
Title
On Seiberg-Witten equationsοn symplectic 4-manifolds
Authors 1
Affiliations
- Institut für Reine Mathematik, Math.-Nat. Fakultät II, Humboldt-Universität zu Berlin, Ziegelstraße 13A, 10099 Berlin, Germany
Abstract
We discuss Taubes' idea to perturb the monopole equations on symplectic manifolds to compute the Seiberg-Witten invariants in the light of Witten's symmetry trick in the Kähler case.
Bibliography
- [A] M. Audin, Exemples de variétés presque complexes, Enseign. Math. (2) 37 (1991), 175-190.
- [BGV] N. Berline, E. Getzler, M. Vergne, Heat Kernels and the Dirac Operators, Grundlehren der Mathematischen Wissenschaften, Springer 1991.
- [FM] R. Friedman, J. W. Morgan, Algebraic surfaces and Seiberg-Witten invariants, alg-geom/9502026, 1995.
- [F] Th. Friedrich, Neue Invarianten der 4-dimensionalen Mannigfaltigkeiten, SFB 288-Preprint 156, 1995.
- [G] M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347.
- [KM] P. B. Kronheimer, T. S. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Lett. 1 (1994), 797-808.
- [LB] C. LeBrun, Einstein Metrics and Mostow Rigidity, Math. Res. Lett. 2 (1995), 1-8.
- [D] D. McDuff, Rational and ruled symplectic 4-manifolds and Erratum, J. Amer. Math. Soc. 3 (1992), 988-997.
- [T] C. H. Taubes, The Seiberg-Witten Invariants and Symplectic Forms, Math. Res. Lett. 1 (1994), 809-822.
- [T1] C. H. Taubes, More Constraints on Symplectic Forms from Seiberg-Witten Invariants, Math. Res. Lett. 2 (1995), 9-14.
- [T2] C. H. Taubes, The Seiberg-Witten and the Gromov invariants, Math. Res. Lett. 2 (1995), 221-238.
- [W] E. Witten, Monopoles and 4-Manifolds, Math. Res. Lett. 1 (1994), 769-796.