  We give a presentation for the Floer cohomology ring $HF^*(\Sigma \times
S^1)$, where $\Sigma$ is a Riemann surface of genus bigger than one, which
coincides with the conjectural presentation for the quantum cohomology ring of
the moduli space of flat SO(3)-connections of odd degree over $\Sigma$. We
study the spectrum of the action of the homology of $\Sigma$ on the Floer
cohomology and prove a physical assumption made by Vafa et al.
