Smoothly embedded spheres in symplectic 4manifolds
Author:
TianJun Li
Journal:
Proc. Amer. Math. Soc. 127 (1999), 609613
MSC (1991):
Primary 57Rxx
MathSciNet review:
1459135
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References 
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Additional Information
Abstract: We characterize rational or ruled surfaces among all symplectic 4manifolds by the existence of certain smoothly embedded spheres.
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 R. Brussee, Some properties of Kahler surfaces, preprint.
 [FS1]
 R. Fintushel and R. Stern, Immersed spheres in 4manifolds and the immersed Thom conjecture, Turkish J. Math. 19 (1995), 145157. MR 96j:57036
 [FS2]
 R. Fintushel and R. Stern, Knots, links, and 4manifolds, preprint.
 [FM]
 R. Friedman and J. Morgan, Algebraic surfaces and SeibergWitten invariants, J. Algebraic Geom. 6 (1997), 445479. CMP 98:05
 [KM]
 P. Kronheimer and T. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Letters 1 (1994), 797808. MR 96a:57073
 [Liu]
 A. Liu, Some new applications of the general wall crossing formula, Math. Res. Letters 3 (1996), 569585. MR 97k:57038
 [LL]
 T. J. Li and A. Liu, Symplectic structures on ruled surfaces and a generalized adjunction inequality, Math. Res. Letters 2 (1995), 453471. MR 96m:57052
 [M1]
 D. McDuff, The structure of rational and ruled symplectic 4manifolds, J. Amer. Math. Soc. 1 (1990), 679710. MR 91k:58042; MR 93k:58098
 [M2]
 D. McDuff, The local behavior of holomorphic curves in almost complex 4manifolds, J. Diff. Geom. 34 (1991), 143164. MR 93e:53050
 [M3]
 D. McDuff, Immersed spheres in symplectic 4manifolds, Ann. Inst. Fourier, Grenoble 42 (1992), 369392. MR 93k:53030
 [M4]
 D. McDuff, Lectures on Gromov invariants for symplectic 4manifolds (Proc. NATO Summer School, Montreal), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 488, Kluwer Acad. Publ., Dordrecht, 1997, pp. 175210. CMP 97:16
 [MS]
 holomorphic curves and quantum cohomology, Univ. Lecture Series Vol. 6.
 [R]
 Y. Ruan, Symplectic topology and complex surfaces, Geometry and Topology on Complex surfaces, ed. Mabuchi, Noguchi, Ochial, World Scientific Publications, Singapore, 1994. CMP 97:16
 [RT]
 Y. Ruan and G. Tian, A mathematical theory of quantum cohomology, J. Diff. Geom. 42 (1995), 259367. MR 96m:58033
 [T1]
 C. H. Taubes, The SeibergWitten invariants and symplectic forms, Math. Res. Letters 1 (1994), 809822. MR 95j:57039
 [T2]
 C. H. Taubes, From the SeibergWitten equations to pseudoholomorphic curves, J. Amer. Math. Soc. 9 (1996), 845918. MR 97a:57033
 [W]
 E. Witten, Monopoles and four manifolds, Math. Res. Letters 1 (1994), 769796. MR 96d:57035
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Additional Information
TianJun Li
Affiliation:
Department of Mathematics, Yale University, New Haven, Connecticut 06520
Email:
tli@math.yale.edu
DOI:
http://dx.doi.org/10.1090/S0002993999044573
PII:
S 00029939(99)044573
Received by editor(s):
January 31, 1997
Received by editor(s) in revised form:
April 4, 1997
Communicated by:
Ronald A. Fintushel
Article copyright:
© Copyright 1999
American Mathematical Society
