Donaldson invariants for nonsimply connected manifolds

Details Donaldson invariants for nonsimply connected manifolds Donaldson invariants for nonsimply connected manifolds

1998-04-15

arxiv.org/abs/hep-th/9804104v2

Commun.Math.Phys. 203 (1999) 249

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, harvmac b-mode, equation (5.17) corrected, two equations added

Scientific paper

10.1007/s002200050611

We study Coulomb branch (``u-plane'') integrals for $\CN=2$ supersymmetric $SU(2),SO(3)$ Yang-Mills theory on 4-manifolds $X$ of $b_1(X)>0, b_2^+(X)=1$. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with $b_1(X)>0, b_2^+(X)>0$. Explicit expressions for $X=\IC P^1 \times F_g$, where $F_g$ 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.

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