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Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds I

An-Min Li·Yongbin Ruan
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Abstract

We define relative Gromov-Witten invariants and establish a general gluing theory of pseudo-holomorphic curves for symplectic cutting and contact surgery. Then, we use our general gluing theory to study the change of GW-invariants of Calabi-Yau 3-folds tranform under flops and extremal transitions. We prove a complete formula for the change of GW-invariants of any genus transform under flop and a general type I extremal transition. Other extremal transition will be handled in a subsequent paper.

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BibTeXRIS

An-Min Li, Yongbin Ruan. 2000-06-29. Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds I. https://arxiv.org/abs/math/9803036

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