Relative Gromov-Witten Invariants

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.

AMS-LaTeX, 52 pages published version

References in corpus (4)

• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Higher genus symplectic invariants and sigma model coupled with gravity
• The Symplectic Sum Formula for Gromov-Witten Invariants
• Complex Curves in Almost-Complex Manifolds and Meromorphic Hulls

Cited by in corpus (6)

• Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
• Hodge integrals and Hurwitz numbers via virtual localization
• Topological recursive relations in $H^{2g}(M_{g,n})$
• Holomorphic disks and topological invariants for closed three-manifolds
• A degeneration of stable morphisms and relative stable morphisms
• The Gromov-Witten potential of a point, Hurwitz numbers, and Hodge integrals