Abstract
The existence of an effective S1-action on a 4-dimensional manifold gives restrictions on the cup-product structure of \(H^*(M;\Bbb Z )\). In generalizing results of R. Fintushel and W. Huck we prove that the symmetric form on \(H^2(M;\Bbb Z )\)/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 S1-action, which has at most 4 different orbit types near every fixed point.
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