The linking pairings of orientable Seifert manifolds

We compute the p-primary components of the linking pairings of orientable 3-manifolds admitting a fixed-point free S 1 -action. Any linking pairing on a finite abelian group of odd order is realized by such a manifold. We find necessary and sufficient conditions for a pairing on an abelian 2-group to be the 2-primary component of such a linking pairing, and give simple examples which are not realizable by any Seifert fibred 3-manifold.