The symplectic sum formula for Gromov-Witten invariants

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Abstract

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.

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Ionel, E. N., & Parker, T. H. (2004). The symplectic sum formula for Gromov-Witten invariants. Annals of Mathematics, 159(3), 935–1025. https://doi.org/10.4007/annals.2004.159.935

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