  The main results of this paper describes a formula for the Seiberg-Witten
invariant of a 4-manifold which admits a nontrivial free S^1-action. We use
this theorem to produce a nonsymplectic 4-manifold with a free circle action
whose orbit space fibers over S^1. We also describe a 3-manifold which is not
the orbit space of any symplectic 4-manifold with a free circle action. A
corollary of the main theorem is a formula for the 3-dimensional Seiberg-Witten
invariants of the total space of a circle bundle over a surface.
