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Seiberg–Witten Invariant of the Universal Abelian Cover of $${S_{-p/q}^{3}(K)}$$

In: Singularities and Computer Algebra

Author

Listed:
  • József Bodnár

    (Stony Brook University, Department of Mathematics)

  • András Némethi

    (Hungarian Academy of Sciences, A. Rényi Institute of Mathematics)

Abstract

We prove an additivity property for the normalized Seiberg–Witten invariants with respect to the universal abelian cover of those 3-manifolds, which are obtained via negative rational Dehn surgeries along connected sum of algebraic knots. Although the statement is purely topological, we use the theory of complex singularities in several steps of the proof. This topological covering additivity property can be compared with certain analytic properties of normal surface singularities, especially with functorial behaviour of the (equivariant) geometric genus of singularities. We present several examples in order to find the validity limits of the proved property, one of them shows that the covering additivity property is not true for negative definite plumbed 3-manifolds in general.

Suggested Citation

  • József Bodnár & András Némethi, 2017. "Seiberg–Witten Invariant of the Universal Abelian Cover of $${S_{-p/q}^{3}(K)}$$," Springer Books, in: Wolfram Decker & Gerhard Pfister & Mathias Schulze (ed.), Singularities and Computer Algebra, pages 173-197, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-28829-1_9
    DOI: 10.1007/978-3-319-28829-1_9
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