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

József Bodnár () and András Némethi ()
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József Bodnár: Stony Brook University, Department of Mathematics
András Némethi: Hungarian Academy of Sciences, A. Rényi Institute of Mathematics

A chapter in Singularities and Computer Algebra, 2017, pp 173-197 from Springer

Abstract: 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.

Keywords: 3-Manifolds; Abelian coverings; Geometric genus; Lattice cohomology; Links of singularities; Normal surface singularities; Plumbed 3-manifolds; $$\mathbb{Q}$$ -Homology spheres; Seiberg–Witten invariants; Superisolated singularities; Surgery 3-manifolds; Primary. 32S05; 32S25; 32S50; 57M27; Secondary. 14Bxx; 32Sxx; 57R57; 55N35 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-28829-1_9

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DOI: 10.1007/978-3-319-28829-1_9

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