Seiberg--Witten invariants and surface singularities

Details Seiberg--Witten invariants and surface singularities Seiberg--Witten invariants and surface singularities

2001-11-29

arxiv.org/abs/math/0111298v3

Geom. Topol. 6(2002) 269-328

Mathematics

Algebraic Geometry

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper9.abs.html

Scientific paper

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.

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