{
  "id": "math/0201034",
  "version": "v2",
  "published": "2002-01-07T04:01:05.000Z",
  "updated": "2002-02-10T23:08:52.000Z",
  "title": "Seiberg-Witten vanishing theorem for $S^1$-manifolds with fixed points",
  "authors": [
    "Scott Baldridge"
  ],
  "comment": "Includes new theorem classifying symplectic 4-manifolds with circle actions having fixed points. Minor updates to existing proofs to reflect the new theorem. 7 pages, 2 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "In this paper we show that the Seiberg--Witten invariant is zero for all smooth 4--manifolds with $b_+{>}1$ which admit circle actions that have at least one fixed point. Furthermore, we show that all symplectic 4--manifolds which admit circle actions with fixed points are rational or ruled, and thus admit a symplectic circle action.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-02-10T23:08:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R57",
      "57M60"
    ],
    "keywords": [
      "fixed point",
      "seiberg-witten vanishing theorem",
      "admit circle actions",
      "symplectic circle action",
      "seiberg-witten invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1034B"
    }
  }
}