Virtual neighborhood technique for moduli spaces of holomorphic curves

We use the technique of Ruan (1999) and Li and Ruan (2001) to construct the virtual neighborhoods and show that the Gromov-Witten invariants can be defined as integrals over the top strata of the virtual neighborhoods. We prove that the invariants defined in this way satisfy all the axioms of Gromov-Witten invariants summarized by Kontsevich and Manin (1994).