{
  "id": "1005.5473",
  "version": "v3",
  "published": "2010-05-29T18:30:51.000Z",
  "updated": "2011-02-06T16:36:02.000Z",
  "title": "The nonorientable four-genus of knots",
  "authors": [
    "Patrick M. Gilmer",
    "Charles Livingston"
  ],
  "comment": "20 pages; expository changes",
  "journal": "J. Lond. Math. Soc. (2) 84 (2011), no. 3, 559-577",
  "doi": "10.1112/jlms/jdr024",
  "categories": [
    "math.GT"
  ],
  "abstract": "We develop obstructions to a knot K in the 3-sphere bounding a smooth punctured Klein bottle in the 4-ball. The simplest of these is based on the linking form of the 2-fold branched cover of the 3-sphere branched over K. Stronger obstructions are based on the Ozsvath-Szabo correction term in Heegaard-Floer homology, along with the G-signature theorem and the Guillou-Marin generalization of Rokhlin's theorem. We also apply Casson-Gordon theory to show that for every n greater than one there exists a knot that does not bound a topologically embedded nonorientable ribbon surface F in the 4-ball with first Betti number less than n.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-02-06T16:36:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "nonorientable four-genus",
      "first betti number",
      "smooth punctured klein bottle",
      "ozsvath-szabo correction term",
      "g-signature theorem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.5473G"
    }
  }
}