Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Smoothly embedded spheres in symplectic 4-manifolds

Author(s): Tian-Jun Li
Journal: Proc. Amer. Math. Soc. 127 (1999), 609-613.
MSC (1991): Primary 57Rxx
MathSciNet review: 1459135
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We characterize rational or ruled surfaces among all symplectic 4-manifolds by the existence of certain smoothly embedded spheres.

References:

[B]
R. Brussee, Some $C^\infty$-properties of Kahler surfaces, preprint.

[FS1]
R. Fintushel and R. Stern, Immersed spheres in 4-manifolds and the immersed Thom conjecture, Turkish J. Math. 19 (1995), 145-157. MR 96j:57036

[FS2]
R. Fintushel and R. Stern, Knots, links, and 4-manifolds, preprint.

[FM]
R. Friedman and J. Morgan, Algebraic surfaces and Seiberg-Witten invariants, J. Algebraic Geom. 6 (1997), 445-479. CMP 98:05

[KM]
P. Kronheimer and T. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Letters 1 (1994), 797-808. MR 96a:57073

[Liu]
A. Liu, Some new applications of the general wall crossing formula, Math. Res. Letters 3 (1996), 569-585. 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), 453-471. MR 96m:57052

[M1]
D. McDuff, The structure of rational and ruled symplectic 4-manifolds, J. Amer. Math. Soc. 1 (1990), 679-710. MR 91k:58042; MR 93k:58098

[M2]
D. McDuff, The local behavior of holomorphic curves in almost complex 4-manifolds, J. Diff. Geom. 34 (1991), 143-164. MR 93e:53050

[M3]
D. McDuff, Immersed spheres in symplectic 4-manifolds, Ann. Inst. Fourier, Grenoble 42 (1992), 369-392. MR 93k:53030

[M4]
D. McDuff, Lectures on Gromov invariants for symplectic 4-manifolds (Proc. NATO Summer School, Montreal), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 488, Kluwer Acad. Publ., Dordrecht, 1997, pp. 175-210. CMP 97:16

[MS]
$J$-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), 259-367. MR 96m:58033

[T1]
C. H. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Letters 1 (1994), 809-822. MR 95j:57039

[T2]
C. H. Taubes, $SW\to Gr:$ From the Seiberg-Witten equations to pseudo-holomorphic curves, J. Amer. Math. Soc. 9 (1996), 845-918. MR 97a:57033

[W]
E. Witten, Monopoles and four manifolds, Math. Res. Letters 1 (1994), 769-796. MR 96d:57035

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57Rxx

Retrieve articles in all Journals with MSC (1991): 57Rxx

Additional Information:

Tian-Jun Li
Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520
Email: tli@math.yale.edu

DOI: 10.1090/S0002-9939-99-04457-3
PII: S 0002-9939(99)04457-3
Received by editor(s): January 31, 1997
Received by editor(s) in revised form: April 4, 1997
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 1999, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia