Donaldson invariants for non-simply connected manifolds

Abstract

We study Coulomb branch ("u-plane") integrals for N = 2 supersymmetric SU (2), SO (3) Yang-Mills theory on 4-manifolds X of b1 (X) > 0, b2+ (X) = 1. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with b1 (X) > 0, b2+ (X) > 0. Explicit expressions for X = ℂ P1 × Fg, where Fg is a Riemann surface of genus g are obtained using Kronecker's double series identity. The result might be useful in future studies of quantum cohomology.