Abstract
The localization technique has been proved to be a useful tool in studying the Gromov-Witten invariants as was shown in the proof of the MarinoVafa formula and a new proof of the Witten conjecture/Kontsevich theorem. Especially when applied to the relative stable moduli, it allows us to express the Gromov-Witten invariants in terms of other invariants such as double Hurwitz numbers or another type of Gromov-Witten invariants. In this paper, we present a universal method to obtain recursion relations on the Gromov-Witten type invariants: let ω ∈ H∗(X) be any natural cohomology class on the target space X , we can determine the Gromov-Witten invariants ∫
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