Relative Gromov–Witten invariants

Authors:
  • EIEleny-Nicoleta Ionel
    Eleny-Nicoleta Ionel
  • TPThomas Parker
    Thomas Parker
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Abstract
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.