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SU(2)-Donaldson invariants of the complex projective plane

  • Michael Griffin EMAIL logo , Andreas Malmendier and Ken Ono
Published/Copyright: July 5, 2015

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 theory with non-trivial Stiefel–Whitney class. In 1997 Moore and Witten conjectured that the regularized u-plane integral on ℂP2 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 claim for the SU(2)-gauge theory. As a consequence, we find that the SU(2)-Donaldson invariants for ℂP2 are explicit linear combinations of the Hurwitz class numbers which arise in the theory of imaginary quadratic fields and orders.

Funding source: National Science Foundation

Funding source: Asa Griggs Candler Fund

Received: 2013-1-23
Revised: 2013-5-13
Published Online: 2015-7-5
Published in Print: 2015-7-1

© 2015 by De Gruyter

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  3. On the sum of two integral squares in certain quadratic fields
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  6. The second main theorem for entire curves into Hilbert modular surfaces
  7. L norms of holomorphic modular forms in the case of compact quotient
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