Michael Griffin

Affiliation: Emory University

Email: mjgrif3@emory.edu

Title Of Talk: SU(2)-Donaldson Invariants of the Complex Projective Plane

URL: http://arxiv.org/abs/1209.2743

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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