The symplectic sum formula for Gromov–Witten invariants

@article{Ionel2000TheSS,
  title={The symplectic sum formula for Gromov–Witten invariants},
  author={Eleny-Nicoleta Ionel and Thomas H. Parker},
  journal={Annals of Mathematics},
  year={2000},
  volume={159},
  pages={935-1025}
}
In the symplectic category there is a 'connect sum' operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula for the Gromov-Witten invariants of a symplectic sum Z = X#Y in terms of the relative GW invariants of X and Y. Several applications to enumerative geometry are given. Gromov-Witten invariants are counts of holomorphic maps into symplectic manifolds. To define them on a symplectic manifold (X,w) one… Expand

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