• Medientyp: E-Artikel
  • Titel: SU(2)-Donaldson invariants of the complex projective plane
  • Beteiligte: Griffin, Michael; Malmendier, Andreas; Ono, Ken
  • Erschienen: Walter de Gruyter GmbH, 2015
  • Erschienen in: Forum Mathematicum, 27 (2015) 4, Seite 2003-2023
  • Sprache: Englisch
  • DOI: 10.1515/forum-2013-6013
  • ISSN: 0933-7741; 1435-5337
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  • Beschreibung: Abstract There are two families of Donaldson invariants for the complex projective plane,corresponding to the SU(2)-gauge theory and the SO(3)-gauge theorywith non-trivial Stiefel–Whitney class.In 1997 Moore and Witten conjectured that the regularized u-plane integralon ℂ P 2 $\mathrm {P}^2$ gives the generating functions for these invariants. In earlier work,the second two authors proved the conjecture for the SO(3)-gauge theory.Here we complete the proof of the conjecture by confirming the claimfor the SU(2)-gauge theory. As a consequence, we find that theSU(2)-Donaldson invariants for ℂ P 2 $\mathrm {P}^2$ are explicit linear combinations of the Hurwitz class numbers which arise in the theory of imaginary quadraticfields and orders.