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The closed string A-model is mathematically described by Gromov-Witten invariants of a compact symplectic manifold $X$. The genus 0 GW invariants give the structure of quantum cohomology of $X$, which ...

In http://arxiv.org/PS_cache/hep-th/pdf/9302/9302103v1.pdf physicists calculate (predict) genus one GW invariants of quintic (Table 1) and some other cases (Table 2). Can any body explain to me (...