Relative Gromov-Witten invariants

@article{Ionel1999RelativeGI,
  title={Relative Gromov-Witten invariants},
  author={Eleny-Nicoleta Ionel and Thomas H. Parker},
  journal={Annals of Mathematics},
  year={1999},
  volume={157},
  pages={45-96}
}
We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension-two symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of [IP4]. The main step is the construction of a compact space of ‘V -stable’ maps. Simple special cases include the Hurwitz numbers for algebraic curves and the enumerative invariants of Caporaso and Harris.