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SEIBERG–WITTEN INVARIANTS AND SURFACE SINGULARITIES. II: SINGULARITIES WITH GOOD ${\mathbb C}^*$-ACTION

Published online by Cambridge University Press:  24 May 2004

ANDRÁS NÉMETHI  and
LIVIU I. NICOLAESCU
ANDRÁS NÉMETHI
Affiliation:
Department of Mathematics, Ohio State University, Columbus, OH 43210, USAnemethi@math.ohio-state.edu
LIVIU I. NICOLAESCU
Affiliation:
University of Notre Dame, Notre Dame, IN 46556, USAnicolaescu.1@nd.edu
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Abstract

A previous conjecture is verified for any normal surface singularity which admits a good ${\mathbb C}^*$-action. This result connects the Seiberg–Witten invariant of the link (associated with a certain ‘canonical’ spin$^c$ structure) with the geometric genus of the singularity, provided that the link is a rational homology sphere.

As an application, a topological interpretation is found of the generalized Batyrev stringy invariant (in the sense of Veys) associated with such a singularity.

The result is partly based on the computation of the Reidemeister–Turaev sign-refined torsion and the Seiberg–Witten invariant (associated with any spin$^c$ structure) of a Seifert 3-manifold with negative orbifold Euler number and genus zero.

Keywords

14B0514J1732S2557M2757R57 (primary)14E1532S4557M25 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 593 - 607
Copyright
The London Mathematical Society 2004

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