Symplectic sums and Gromov-Witten invariants

Details Symplectic sums and Gromov-Witten invariants Symplectic sums and Gromov-Witten invariants

2003-04-21

arxiv.org/abs/math/0304298v1

Proceedings of the ICM, Beijing 2002, vol. 2, 427--436

Mathematics

Geometric Topology

Scientific paper

Gromov-Witten invariants of a symplectic manifold are a count of holomorphic curves. We describe a formula expressing the GW invariants of a symplectic sum $X# Y$ in terms of the relative GW invariants of $X$ and $Y$. This formula has several applications to enumerative geometry. As one application, we obtain new relations in the cohomology ring of the moduli space of complex structures on a genus g Riemann surface with n marked points.

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