The Seiberg-Witten invariants of manifolds with wells of negative curvature

Details The Seiberg-Witten invariants of manifolds with wells of negative curvature The Seiberg-Witten invariants of manifolds with wells of negative curvature

2002-05-22

arxiv.org/abs/math/0205234v1

Mathematics

Geometric Topology

Scientific paper

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.

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