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

Using the u-plane integral of Moore and Witten, we derive a simple expression for the Donaldson invariants of product ruled surfaces Σg × S, where Σg is a Riemann surface of genus g. This expression generalizes a theorem of Morgan and Szabó 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 Σg×S.