Journal of the London Mathematical Society



Notes and Papers

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


ANDRÁS NÉMETHI a1 1 and LIVIU I. NICOLAESCU a2 1
a1 Department of Mathematics, Ohio State University, Columbus, OH 43210, USA nemethi@math.ohio-state.edu
a2 University of Notre Dame, Notre Dame, IN 46556, USA nicolaescu.1@nd.edu

Article author query
nemethi a   [Google Scholar] 
nicolaescu l   [Google Scholar] 
 

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.

(Received June 9 2003)
(Revised November 7 2003)

Maths Classification

14B05; 14J17; 32S25; 57M27; 57R57 (primary); 14E15; 32S45; 57M25 (secondary).



Footnotes

1 The first author is partially supported by NSF grant DMS-0088950; the second author is partially supported by NSF grant DMS-0071820.