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

An-Min Li; Yongbin Ruan

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

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arxiv math/9803036 v4 pith:HKMXTNVH submitted 1998-03-10 math.AG hep-thmath.DG

An-Min Li , Yongbin Ruan This is my paper · ORCID

classification math.AGhep-thmath.DG

keywords extremalgeneralcalabi-yauchangefoldsgluinggromov-wittengw-invariants

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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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This paper is a survey of the geometry of conifold transitions between Calabi-Yau threefolds, focusing on non-Kähler outputs and the structures they carry.

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