2001/07/12 by Scott Baldridge, Baldridge, Scott
Mathematics · #57M60 #57R57 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT #msc:57M60 #msc:57R57
paper · pdf · doi:10.48550/arxiv.math/0107092
Latex, 27 pages, 2 figures
arxiv created 2001/07/12 · openalex publication_date 2001/07/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result of this paper is a formula for calculating the Seiberg-Witten invariants of 4-manifolds with fixed-point free circle actions. This is done by showing under suitable conditions the existence of a diffeomorphism between the moduli space of the 4-manifold and the moduli space of the quotient 3-orbifold. Two corollaries include b+>1 4-manifolds with fixed-point free circle actions are simple type and a new proof that the four dimensional invariants of Y × S1 are equal to the the three dimensional invariants of Y. An infinite number of b+=1 4-manifolds where the Seiberg-Witten invariants are still diffeomorphism invariants are constructed and studied.