Donaldson invariants of product ruled surfaces and two-dimensional gauge theories

Details Donaldson invariants of product ruled surfaces and two-dimensional gauge theories Donaldson invariants of product ruled surfaces and two-dimensional gauge theories

1999-07-20

arxiv.org/abs/hep-th/9907165v1

Commun.Math.Phys.220:231-261,2001

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, harvmac b mode

Scientific paper

10.1007/s002200100442

Using the u-plane integral of Moore and Witten, we derive a simple expression for the Donaldson invariants of $\Sigma_g \times S^2$, where $\Sigma_g$ is a Riemann surface of genus g. This expression generalizes a theorem of Morgan and Szabo for g=1 to any genus g. We give two applications of our results: (1) We derive Thaddeus' formulae for the intersection pairings on the moduli space of rank two stable bundles over a Riemann surface. (2) We derive the eigenvalue spectrum of the Fukaya-Floer cohomology of $\Sigma_g \times S^1$.

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