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

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.

Latex, revised version, a much shorter and better written version

References in corpus (5)

• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Higher genus symplectic invariants and sigma model coupled with gravity
• Virtual neighborhoods and pseudo-holomorphic curves
• Deforming Calabi-Yau Threefolds
• The quantum cohomology of homogeneous varieties

Cited by in corpus (6)

• Curve counting via stable pairs in the derived category
• Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
• The number of ramified covering of a Riemann surface by Riemann surface
• Holomorphic disks and topological invariants for closed three-manifolds
• Exponential decay of $J$-holomorphic maps with finite energy
• Local Donaldson-Thomas invariants of Blowups of surfaces