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

Abstract

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 ${\Sigma }_g\times S^1$.

arXiv comment39 pages, harvmac b mode

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