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arXiv · hep-th/9907165

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

Carlos Lozano·Marcos Marino
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Abstract

Using the u-plane integral of Moore and Witten, we derive a simple expression for the Donaldson invariants of $Σ_g \times S^2$, where $Σ_g$ 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 $Σ_g \times S^1$.

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Carlos Lozano, Marcos Marino. 1999-07-20. Donaldson invariants of product ruled surfaces and two-dimensional gauge theories. https://doi.org/10.1007/s002200100442

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