Geodesic
The Seiberg–Witten invariants of negative definite plumbed 3-manifolds
Journal of the European Mathematical Society, Tome 13 (2011) no. 4, pp. 959-974

Voir la notice de l'article provenant de la source EMS Press

Assume that Γ is a connected negative definite plumbing graph, and that the associated plumbed 3-manifold M is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg–Witten invariant of M. The first one is the constant term of a 'multivariable Hilbert polynomial', it reflects in a conceptual way the structure of the graph Γ, and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities. The second formula realizes the Seiberg–Witten invariant as the normalized Euler characteristic of the lattice cohomology associated with Γ, supporting the conjectural connections between the Seiberg–Witten Floer homology, or the Heegaard–Floer homology, and the lattice cohomology.
DOI : 10.4171/jems/272
Classification : 32-XX, 57-XX, 00-XX
Keywords: Normal surface singularities, resolutions of singularities, links of singularities, plumbed 3-manifolds, plumbing graphs, Seiberg–Witten invariants, surgery formulae, periodic constant, Hilbert polynomials, Seiberg–Witten Invariant Conjecture, zeta-function, lattice cohomology, Heegaard-Floer homology 
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     author = {Andr\'as N\'emethi},
     title = {The {Seiberg{\textendash}Witten} invariants of negative definite plumbed 3-manifolds},
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     doi = {10.4171/jems/272},
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András Némethi. The Seiberg–Witten invariants of negative definite plumbed 3-manifolds. Journal of the European Mathematical Society, Tome 13 (2011) no. 4, pp. 959-974. doi: 10.4171/jems/272

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