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Dusa Mc Duff
Immersed spheres in symplectic 4-manifolds
Annales de l'institut Fourier, 42 no. 1-2 (1992), p. 369-392, doi: 10.5802/aif.1296
Article PDF | Reviews MR 93k:53030 | Zbl 0756.53021

Résumé - Abstract

We discuss conditions under which a symplectic 4-manifold has a compatible Kähler structure. The theory of $J$-holomorphic embedded spheres is extended to the immersed case. As a consequence, it is shown that a symplectic 4-manifold which has two different minimal reductions must be the blow-up of a rational or ruled surface.


[BPV] W. BARTH, C. PETERS & A. VAN de VEN, Complex Surfaces, Springer Verlag, 1984.  MR 86c:32026 |  Zbl 0718.14023
[U] H. CLEMENS, J. KOLLAR, S. MORI, Higher dimensional complex geometry, Astérisque, 166 (1989).
[FGG] M. FERNANDEZ, M. GOTAY, A. GRAY, Four dimensional parallelizable symplectic and complex manifolds, Proc. Amer. Math. Soc., 103 (1988), 1209-1212.  MR 90a:53039 |  Zbl 0656.53034
[FM] FRIEDMAN and MORGAN, Diffeomorphism types of 4-manifolds, Journ. Diff. Geo., (1988).
[GR] M. GROMOV, Pseudo-holomorphic curves on almost-complex manifolds, Invent. Math., 82 (1985), 307-347.  MR 87j:53053 |  Zbl 0592.53025
[EX] D. MCDUFF, Examples of symplectic structures, Invent. Math., 89 (1987), 13-36.  MR 88m:58061 |  Zbl 0625.53040
[RR] D. MCDUFF, The Structure of Rational and Ruled Symplectic 4-manifolds, Journ. Amer. Math. Soc., 3 (1990), 679-712.  MR 91k:58042 |  Zbl 0723.53019
[EL] D. MCDUFF, Elliptic methods in symplectic geometry, Bull. Amer. Math. Soc., 23 (1990), 311-358. Article |  MR 91i:58046 |  Zbl 0723.53018
[BL] D. MCDUFF, Blow ups and symplectic embeddings in dimension 4, Topology, 30 (1991), 409-421.  MR 92m:57039 |  Zbl 0731.53035
[LB] D. MCDUFF, The Local Behaviour of holomorphic curves in almost complex 4-manifolds, Journ. Diff. Geom., 34 (1991), 143-164.  MR 93e:53050 |  Zbl 0736.53038
[KY] D. MCDUFF, Symplectic 4-manifolds, to appear in Proceedings of I.C.M., Kyoto, 1990.  MR 94b:57042 |  Zbl 0732.57012
[UB] D. MCDUFF, Remarks on the uniqueness of symplectic blowing up, preprint, 1990.
[RU] D. MCDUFF, Notes on Ruled Symplectic 4-manifolds, preprint, 1992.  Zbl 0810.53020
[PW] T. PARKER and J. WOLFSON, A compactness theorem for Gromov's moduli space, preprint, 1991.
[TH] W. THURSTON, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc., 55 (1976), 467-468.  MR 53 #6578 |  Zbl 0324.53031
[WO] J. WOLFSON, Gromov's compactness of pseudo-holomorphic curves and symplectic geometry, J. Diff. Geom., 28 (1988), 383-405.  MR 89m:53058 |  Zbl 0661.53024
[YE] R. YE, Gromov's Compactness Theorem for Pseudo-holomorphic Curves, preprint, UCSB, 1991.  Zbl 0810.53024