Transfer trajectory design in the restricted three-body problem is largely dependent on the topology of the invariant manifolds of a periodic orbit. In this paper, the behavior of such manifolds are studied through the use of a Poincaré map generated from a zero momentum subspace of the third-body motion. Such maps characterize the regions of allowed motions of the invariant manifolds and are shown to occupy the space bounded by quasi-periodic orbits. The dynamical structures arising from these zero-momentum surfaces are utilized to identify transport opportunities to planar Lyapunov orbits develop a catalog of transfers in cislunar space.