On the construction of certain 6-dimensional symplectic manifolds with Hamiltonian circle actions

Let (M,omega) be a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian S-1 action such that the fixed point set consists of isolated points or surfaces. Assume dim H-2(M) < 3. In an earlier paper, we defined a certain invariant of such spaces which consists of fixed point data and twist type, and we divided the possible values of these invariants into six "types". In this paper, we construct such manifolds with these "types". As a consequence, we have a precise list of the values of these invariants.