The main results of this paper describes a formula for the Seiberg-Witten invariant of a 4-manifold which admits a nontrivial free circle action. We use this theorem to produce a nonsymplectic 4-manifold with a free circle action whose orbit space fibers over circle. We also describe a nontrivial 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. © World Scientific Publishing Company.
Publication Source (Journal or Book title)
Communications in Contemporary Mathematics
Baldridge, S. (2001). Seiberg-Witten invariants of 4-manifolds with free circle actions. Communications in Contemporary Mathematics, 3 (3), 341-353. https://doi.org/10.1142/S021919970100038X