Seiberg–Witten invariants and surface singularities: splicings and cyclic covers

• András Némethi ^[1] ; Liviu I. Nicolaescu ^[2]
  1. [1] Ohio State University

     Ohio State University

     City of Columbus, Estados Unidos

     
  2. [2] University of Notre Dame

     University of Notre Dame

     Township of Portage, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 11, Nº. 3-4, 2006, págs. 399-451
• Idioma: inglés
• DOI: 10.1007/s00029-006-0016-2
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• Resumen

  • We verify the conjecture formulated in [36] for suspension singularities of type g(x, y, z)=f(x, y)+z n , where f is an irreducible plane curve singularity. More precisely, we prove that the modified Seiberg–Witten invariant of the link M of g, associated with the canonical spin c structure, equals −σ(F)/8, where σ(F) is the signature of the Milnor fiber of g. In order to do this, we prove general splicing formulae for the Casson–Walker invariant and for the sign-refined Reidemeister–Turaev torsion. These provide results for some cyclic covers as well. As a by-product, we compute all the relevant invariants of M in terms of the Newton pairs of f and the integer n.