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.

Authors

Eleny-Nicoleta Ionel


Current address:

Department of Mathematics
Stanford University
Stanford, CA 94305-2125 Thomas H. Parker

Department of Mathematics
Michigan State University
East Lansing, MI 48824