2002/05/22 by Daniel Ruberman, Ruberman, Daniel
Mathematics · #53C21 #57R57 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT #msc:53C21 #msc:57R57
paper · pdf · doi:10.48550/arxiv.math/0205234
arxiv created 2002/05/22 · openalex publication_date 2002/05/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the vanishing theorem for the Seiberg-Witten invariants of a manifold with positive scalar curvature to the case when the curvature is allowed to be negative on a set of small volume. (The precise curvature bounds are described in the paper.) The idea is to combine the method of `semigroup domination' with the Weitzenbock formula. The same curvature hypothesis implies the vanishing of the Seiberg-Witten invariant of any finite covering space. We also show that, in high dimensions, a spin manifold with mostly positive scalar curvature in fact admits a metric of positive scalar curvature.