Seiberg–Witten invariants and surface singularities

Némethi, András¹ ; Nicolaescu, Liviu I²

¹ Department of Mathematics, Ohio State University, Columbus, Ohio 43210, USA
² Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, USA

Geometry & topology, Tome 6 (2002) no. 1, pp. 269-328.

Résumé

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.

Détail

DOI : 10.2140/gt.2002.6.269

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

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