  We produce an equality between the Gromov-Witten invariants of the moduli
space M of rank two odd degree stable vector bundles over a Riemann surface
$\Sigma$ and the Donaldson invariants of the algebraic surface $\Sigma \times
P^1$. We discuss on to how extent the Quantum cohomology of M determines its
Gromow-Witten invariants. Finally we find the isomorphism between the usual
cohomology and the Quantum cohomology for the moduli space M over a Riemann
surface of genus g=3.
