{
  "id": "math/0205234",
  "version": "v1",
  "published": "2002-05-22T18:58:38.000Z",
  "updated": "2002-05-22T18:58:38.000Z",
  "title": "The Seiberg-Witten invariants of manifolds with wells of negative curvature",
  "authors": [
    "Daniel Ruberman"
  ],
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-05-22T18:58:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R57",
      "53C21"
    ],
    "keywords": [
      "seiberg-witten invariant",
      "positive scalar curvature",
      "negative curvature",
      "precise curvature bounds",
      "curvature hypothesis implies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......5234R"
    }
  }
}