#### Volume 6, issue 1 (2002)

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Seiberg–Witten invariants and surface singularities

### András Némethi and Liviu I Nicolaescu

Geometry & Topology 6 (2002) 269–328
 arXiv: math.AG/0111298
##### Abstract

We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg–Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we establish its validity for a large class of singularities: some rational and minimally elliptic (including the cyclic quotient and “polygonal”) singularities, and Brieskorn–Hamm complete intersections. Some of the verifications are based on a result which describes (in terms of the plumbing graph) the Reidemeister–Turaev sign refined torsion (or, equivalently, the Seiberg–Witten invariant) of a rational homology 3–manifold $M$, provided that $M$ is given by a negative definite plumbing. These results extend previous work of Artin, Laufer and S S-T Yau, respectively of Fintushel–Stern and Neumann–Wahl.

##### Keywords
(links of) surface singularities, ($\mathbb{Q}$–)Gorenstein singularities, rational singularities, Brieskorn–Hamm complete intersections, geometric genus, Seiberg–Witten invariants of $\mathbb{Q}$–homology spheres, Reidemeister–Turaev torsion, Casson–Walker invariant
##### Mathematical Subject Classification 2000
Primary: 14B05, 14J17, 32S25, 57R57
Secondary: 57M27, 14E15, 32S55, 57M25