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arXiv · 1209.2743

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

Michael Griffin·Andreas Malmendier·Ken Ono
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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 the complex projective plane 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 CP^2 are explicit linear combinations of the Hurwitz class numbers which arise in the theory of imaginary quadratic fields and orders.

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Michael Griffin, Andreas Malmendier, Ken Ono. 2012-09-12. SU(2)-Donaldson invariants of the complex projective plane. https://doi.org/10.1515/forum-2013-6013

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