The Seiberg-Witten invariants of symplectic four-manifolds

Kotschick, Dieter

Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Exposé no. 812, 26 p.

[1] D. Bennequin - Monopoles de Seiberg-Witten et conjecture de Thom [d'après Kronheimer, Mrowka, Witten, ...]. Séminaire Bourbaki, 48ème année 1995-96, n° 807. | Numdam | Zbl | MR | EuDML

[2] O. Biquard - Les équations de Seiberg-Witten sur une surface complexe non kählérienne. Preprint 1995. | MR | Zbl

[3] S. K. Donaldson - The orientation of Yang-Mills moduli spaces and $4$-manifold topology. J. Differential Geometry 26 (1987), 397-428. | Zbl | MR | DOI

[4] S. K. Donaldson - Yang-Mills invariants of four-manifolds. In Geometry of Low-Dimensional Manifolds: 1, ed. S. K. Donaldson and C. B. Thomas, Cambridge Univ. Press 1990. | Zbl | MR

[5] S. K. Donaldson - The Seiberg-Witten equations and 4-manifold topology, Bull. Amer. Math. Soc. 33 (1996), 45-70. | Zbl | MR | DOI

[6] R. Fintushel and R. J. Stern - Immersed spheres in 4-manifolds and the immersed Thom conjecture. Proc. of Gökova Geometry-Topology Conference 1994, Turkish J. of Math. 19 (2) (1995), 27-39. | Zbl | MR

[7] P. Gauduchon - Hermitian connections and Dirac operators. Boll. Un. Mat. Ital. (to appear). | Zbl | MR

[8] R. E. Gompf - A new construction of symplectic manifolds. Annals of Math. 142 (1995), 527-595. | Zbl | MR | DOI

[9] R. E. Gompf and T. S. Mrowka - Irreducible $4$-manifolds need not be complex. Annals of Math. 138 (1993), 61-111. | Zbl | MR | DOI

[10] M. Gromov - Pseudo-holomorphic curves in symplectic manifolds. Invent. Math. 82 (1985), 307-347. | Zbl | MR | EuDML | DOI

[11] K. Kodaira - On the structure of compact complex analytic surfaces, I. Amer. J. Math. 86 (1964), 751-798. | Zbl | MR | DOI

[12] D. Kotschick - On irreducible four-manifolds. Preprint alg-geom/9504012 (unpublished).

[13] D. Kotschick, J. W. Morgan and C. H. Taubes - Four-manifolds without symplectic structures but with non-trivial Seiberg-Witten invariants. Math. Research Letters 2 (1995),119-124. | Zbl | MR | DOI

[14] P. B. Kronheimer and T. S. Mrowka - The genus of embedded surfaces in the projective plane. Math. Research Letters 1 (1994), 797-808. | Zbl | MR | DOI

[15] D. Mcduff and D. Salamon - $J$-holomorphic curves and quantum cohomology. Amer. Math. Soc., Providence 1994. | Zbl | MR | DOI

[16] D. Mumford - An algebraic surface with $K$ ample, $\left(K^2\right)=9,p_g=q=0$. Amer. J. Math. 101 (1979), 233-244. | Zbl | MR | DOI

[17] Y. Ruan - Symplectic topology on algebraic $3$-folds. J. Differential Geometry 39 (1994), 215-227. | Zbl | MR | DOI

[18] C. H. Taubes - The Seiberg-Witten invariants and symplectic forms. Math. Research Letters 1 (1994), 809-822. | Zbl | MR | DOI

[19] C. H. Taubes - More constraints on symplectic manifolds from Seiberg-Witten invariants. Math. Research Letters 2 (1995), 9-14. | Zbl | MR | DOI

[20] C. H. Taubes - Seiberg-Witten equations and symplectic geometry. Lecture at the conference on Seiberg-Witten invariants, Princeton, January 16th, 1995.

[21] C. H. Taubes - The Seiberg-Witten and the Gromov invariants. Math. Research Letters 2 (1995), 221-238. | Zbl | MR | DOI

[22] C. H. Taubes - $SW\Rightarrow Gr$, From the Seiberg-Witten equations to pseudo-holomorphic curves. Jour. Amer. Math. Soc. 9 (1996), 845-918. | Zbl | DOI

[23] C. H. Taubes - Counting pseudo-holomorphic submanifolds in dimension $4$. J. Differential Geometry (to appear). | Zbl | MR

[24] C. H. Taubes - $Gr\Rightarrow SW$, From pseudo-holomorphic curves to Seiberg-Witten solutions. Preprint 1996. | Zbl

[25] C. H. Taubes - (in preparation).

[26] W. P. Thurston - Some simple examples of symplectic manifolds. Proc. Amer. Math. Soc. 55 (1976), 467-468. | Zbl | MR

[27] A. Weil - Introduction à l'étude des variétés kählériennes, Hermann, Paris 1958. | Zbl | MR

[28] E. Witten - Monopoles and four-manifolds. Math. Research Letters 1 (1994), 769- 796. | Zbl | MR | DOI