{
  "id": "1305.7492",
  "version": "v4",
  "published": "2013-05-31T17:25:55.000Z",
  "updated": "2015-03-08T11:30:33.000Z",
  "title": "A construction of slice knots via annulus twists",
  "authors": [
    "Tetsuya Abe",
    "Motoo Tange"
  ],
  "comment": "26 pages and 28 figures. Comments are welcome.Version 2: A new section added. Version 3: The definition of an annulus twist was clarified. The anonymous referee pointed out a gap of Theorem 3.1. The statement of Theorem 3.1 was weakened. Version 4: Abstract, Introduction and Section 6 are rewritten",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give a new construction of slice knots via annulus twists. The simplest slice knots obtained by our method are those constructed by Omae. In this paper, we introduce a sufficient condition for given slice knots to be ribbon, and prove that all Omae's knots are ribbon.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-05T05:29:36.000Z",
      "abstract": "We give a new construction of slice knots via annulus twists which provides potential counterexamples to the slice-ribbon conjecture. Among them, the knots constructed by Omae are the simplest ones. In our previous work, we proved that one of them is a ribbon knot. In this paper, we prove that the rest are also ribbon knots.",
      "comment": "22 pages and 24 figures. Comments are welcome.Version 2: Corollary 3.2 and a new section added. Version 3: The definition of an annulus twist was clarified. The anonymous referee pointed out a gap of the main theorem(Theorem 3.1). The statement of Theorem 3.1 was weakened. The original goal, to construct potential counterexamples to the slice-ribbon conjecture, is still achieved",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-03-08T11:30:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57R65"
    ],
    "keywords": [
      "slice knots",
      "annulus twists",
      "construction",
      "ribbon knot"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.7492A"
    }
  }
}