2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79366The 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.LaTex, 13 pages, 2 figuresGeometric TopologyDifferential Geometry57R57; 57M60text