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Genus Minimizing in Symplectic 4-Manifolds

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Abstract

The authors show that a symplectically embedded surface in a symplectic 4-manifold with b +2 greater than one minimizes genus in its homology class.

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References

  1. Auckly, D., Homotopy K3 surfaces and gluing results in Seiberg-Witten theory, Three lectures for the GARC, 1996.

  2. Cho, Y. S., Seiberg-Witten invariants on non-symplectic 4-manifolds, to appear in Osaka J. Math..

  3. Cho, Y. S., Finite group actions on Spin c bundles, Acta Math. Hungar., 84:1–2(1999), 97–114.

    Article  MathSciNet  Google Scholar 

  4. Cho, Y. S., Generalized Thom Conjecture for almost complex manifolds, Preprint.

  5. Cho, Y. S., Finite group actions on the moduli space of self-dual connections (I), Thins. A. M. S., 323:1(1991), 233–261.

    Article  MathSciNet  Google Scholar 

  6. Cho, Y. S., Equivariant metrics for smooth moduli spaces, Topology and its Applications, 62(1995), 77–85.

    Article  MathSciNet  Google Scholar 

  7. Cho, M. S. & Cho, Y. S., The geography of simply connected symplectic manifolds, Preprint.

  8. Donaldson, S., The Seiberg-Witten equations and 4-manifold topology, Bull. of A. M. S., 33:1(1995), 45–70.

    Article  MathSciNet  Google Scholar 

  9. Kirby, R., Problems in low-dimensional topology, Berkeley, 1995.

  10. Kronheimer, P. & Mrowka, T., The geuns of embedded surfaces in the projective plane, Math. Res. Lett., 1(1994), 797–808.

    Article  MathSciNet  Google Scholar 

  11. McDuff, D., The structure of rational and ruled symplectic 4-manifolds, Jour. of A. M. S., 3(1990), 679–712.

    MathSciNet  Google Scholar 

  12. McDuff, D. & Salamon, D., Introduction to symplectic topology, Clarendon Press, Oxford, 1995.

  13. Morgan, J., Szabó, Z. & Taubes, C., A product formula for the Seiberg-Witten invariants and the generalized Thom Conjecture, Preprint, 1995.

  14. Taubes, C., The Seiberg-Witten invariants and symplectic forms, Math. Res. Lett., 1(1994), 809–822.

    Article  MathSciNet  Google Scholar 

  15. Taubes, C., The Seinerg-Witten invariants and Gromov invariants, Math. Res. Lett., 1(1994), 221–238.

    Google Scholar 

  16. Taubes, C., From the Seiberg-Witten equations to pseudd-holomorphic curves, Preprint.

  17. Witten, E., Monopoles and 4-manifolds, Math. Res. Lett., 1(1994), 769–796.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Ewha Women’s University, Seoul, 120-750, Korea

    Yongseung Cho & Misung Cho

Authors
  1. Yongseung Cho
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  2. Misung Cho
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Additional information

Project supported by the MOST through National R and D Program (98-N6-01-01-A-1) for Women’s University of Korea.

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Cho, Y., Cho, M. Genus Minimizing in Symplectic 4-Manifolds. Chin. Ann. of Math. 21, 115–120 (2000). https://doi.org/10.1007/BF02731965

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  • DOI: https://doi.org/10.1007/BF02731965

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