| There have been several versions of relative Gromov-Witten invariants which count holomorphic curves in a manifold relative to some submanifold. The Symplectic Field Theory of Eliashberg, Givental, and Hofer uses analytic methods to construct invariants which are organized in generating functions. The Relative Gromov-Witten invariants of Li are constructed through algebraic geometric methods.; In this thesis, we use Li's method to construct generating functions of invariants analogous to those in Symplectic Field Theory. By studying line bundles on moduli spaces, we are able to prove a number of degeneration formulae that give relations between these generating functions. By using these relations, we are able to construct a homology theory analogous to that of Symplectic Field Theory.; We apply our formalism to a number of classical cases and re-derive some well-known degeneration formulae. |
