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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
Entstehung:
Anmerkungen:
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.