Ring structure of the Floer Cohomology of $Σ\times S^1$

Mathematics – Differential Geometry

Scientific paper

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13 pages, Latex2e

Scientific paper

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.

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