  We use virtual neighborhood technique to establish GW-invariants, Quantum
cohomology, equivariant GW-invariants, equivariant quantum cohomology and Floer
cohomology for general symplectic manifold. We also establish GW-invariants for
a family of symplectic manifolds. As a consequence, we prove Arnold conjecture
for nondegenerate Hamiltonian symplectomorphisms.
