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Journal of the London Mathematical Society 2004 69(3):593-607; doi:10.1112/S0024610704005228
© 2004 by London Mathematical Society
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© The London Mathematical Society

Seiberg–Witten Invariants and Surface Singularities. II: Singularities with Good C*-Action

András Némethi and Liviu I. Nicolaescu

Department of Mathematics, Ohio State University Columbus, OH 43210, USA, nemethi{at}math.ohio-state.edu
University of Notre Dame Notre Dame, IN 46556, USA, nicolaescu.1{at}nd.edu

Received 9 June 2003. Revision received 7 November 2003.

A previous conjecture is verified for any normal surface singularity which admits a good C*-action. This result connects the Seiberg–Witten invariant of the link (associated with a certain ‘canonical’ spinc 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 spinc structure) of a Seifert 3-manifold with negative orbifold Euler number and genus zero.


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