RELATIVE GROMOV-WITTEN INVARIANTS OF ℂℙ2 AND ℙ1 × ℙ1

In this thesis we present the explicit formula of relative Gromov-Witten of (P¹×P¹,diagonal), motivated by the work of Fan and Wu. Furthermore, due to the closed form of the generating functions of these Gromov-Witten invariants, we are able to deduce the asymptotic expansions of relative Gromov-Witten invariants of (P¹*P¹,diagonal) and $(CP²,conic)$ and reveal the underlying relation of these two sets of relative Gromov-Witten invariants.

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