Circle actions on 4-manifolds II

The existence of an effective S-1-action on a 4-dimensional manifold gives restrictions on the cup-product structure of H*(M; Z). In generalizing results of R. Fintushel and W. Huck we prove that the symmetric form on H-2(M; Z)/torsion given by the cup-product (and a chosen orientation) decomposes into a direct sum of forms of rank 1 or 2, if the closed, orientable 4-manifold M admits a non-trivial S-1-action, which has at most 4 different orbit types near every fixed point.