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Commentarii Mathematici Helvetici

, Volume 74, Issue 4, pp 575–590 | Cite as

Simple singularities and topology of symplectically filling 4-manifold

  • H. Ohta
  • K. Ono

Abstract.

Topological restrictions of symplectically filling 4-manifolds of links around simple singularities are studied by using the Seiberg-Witten monopole equations. In particular, the intersection form of minimal symplectically filling 4-manifolds of the singularity of type E 8 is determined. Moreover, for the case of simply elliptic singularities, similar restrictions are obtained. In the proof, a vanishing theorem of the Seiberg-Witten invariant is discussed.

Key words. Fillable contact structure, symplectic filling, simple singularity, simply elliptic singularity, the Seiberg-Witten monopole equations. 

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Copyright information

© Birkhäuser Verlag, Basel, 1999

Authors and Affiliations

  • H. Ohta
    • 1
  • K. Ono
    • 2
  1. 1.Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan, e-mail: ohta@math.nagoya-u.ac.jpJP
  2. 2.Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan, e-mail: ono@math.sci.hokudai.ac.jpJP

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