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    ×
  • Bulletin of the Australian Mathematical Society, Volume 56, Issue 3
  • December 1997, pp. 363-384

Seiberg-Witten invariants of generalised rational blow-downs

  • Jongil Park (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972700031154
  • Published online: 01 April 2009
Abstract

One of the main problems in Seiberg-Witten theory is to find (SW)-basic classes and their invariants for a given smooth 4-manifold. The rational blow-down procedure introduced by Fintushel and Stern is one way to compute these invariants for some smooth 4-manifolds. In this paper, we extend their results to the general case. That is, we find (SW)-basic classes and Seiberg-Witten invariants for generalised rational blow-down 4-manifolds by using index computations.

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[2]A. Casson and J. Harer , ‘Some homology lens spaces which bound rational homology balls’, Pacific J. Math. 96 (1981), 2336.

[6]R. Gompf , ‘Nuclei of elliptic surfaces’, Topology 30 (1991), 479511.

[8]P. Kronheimer and T. Mrowka , ‘The genus of embedded surfaces in the projective plane’, Math. Res. Lett. 1 (1994), 797808.

[10]E. Witten , ‘Monopoles and four-manifolds’, Math. Res. Lett. 1 (1994), 769796.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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