• Cho, Yong-Seung (Department of Mathematical and Institute for Mathematical Sciences, Ewha Women’s University)
  • Published : 2003.11.01


Let X be a 4-manifold obtained by gluing two symplectic 4-manifolds Xi, i = 1, 2, along embedded surfaces. Using the gradient flow of a functional on 3-dimensional Seiberg-Witten theory along the cylindrical end, we study the Seiberg-Witten equations on X and have a product formula of Seiberg-Witten invariants on X from the ones on Xi, i = 1, 2.


  1. progress in Math. v.117 Holomorphic curves in symplectic geometry M.Audin;J.Lafontaine
  2. Osaka J. Math. v.34 Seiberg-Witten invariants on non-symplectic 4-manifolds Y.S.Cho
  3. Geometry of Low dimensional Manifolds, Proceedings of the Durham Symposium Yang-Mills Invariants of Four-manifolds S.K.Donaldson
  4. Turkish J. Math. v.19 no.2 Immersed sphere in 4-manifolds and the immersed Thom conjecture R.Fintushed;R.Stern
  5. Comm. Math. Phys. v.118 An instanton-invariant for 3-manifold A.Floer
  6. Invent. Math. v.82 Psuedoholomorphic curves in symplectic manifolds M.Gromov
  7. Internat. Math. Res. Notices no.6 On connected sum decompositions of algebraic surfaces and their fundamental group D.Kotschick
  8. On irreducible four manifolds D.Kotschick
  9. Math. Res. Lett. v.1 The genus of embedded surfaces in the projective plane P.Kronheimer;T.Mrowka
  10. Math. Res. Lett. v.2 Four manifolds without symplectic structures but nontrivial Seiberg-witten invariants D.Kotschick;J.Morgan;C.Taubes
  11. Spin Geometry B.Lawson;M.Michelshon
  12. University Lecture series v.6 J-holomorphic curves and quantum cohomology D.McDuff;D.Salamon
  13. J. Differential Geom v.44 A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture J.Morgan;Z.Szabo;C.Taubes
  14. Geometry and Seiberg-Witten invariant D.Salamon
  15. Math. Res. Lett. v.2 More constraints on symplectic manifolds from Seiberg-Witten equations C.Taubes
  16. From the Seiberg-Witten Invariants to Pseudo-holomorphic curves C.Taubes
  17. Product formula for the SW invariants and the generalized Thom conjecture C.Taubes