{
  "id": "1502.06352",
  "version": "v1",
  "published": "2015-02-23T09:05:02.000Z",
  "updated": "2015-02-23T09:05:02.000Z",
  "title": "On the Morse-Novikov number for 2-knots",
  "authors": [
    "Hisaaki Endo",
    "Andrei Pajitnov"
  ],
  "comment": "Latex, 14 pages",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Let $K\\subset S^4$ be a 2-knot, that is, a smoothly embedded 2-sphere in $S^4$. The Morse-Novikov number $\\mathcal M\\mathcal N(K)$ is the minimal possible number of critical points of a Morse map $S^4\\setminus K\\to S^1$ belonging to the canonical class in $H^1(S^4\\setminus K)$. We prove that for a classical knot $K\\subset S^3$ the Morse-Novikov number of the spun knot $S(K)$ is $\\leq 2\\mathcal M\\mathcal N(K)$. This enables us to compute $\\mathcal M\\mathcal N(S(K))$ for every classical knot $K$ with tunnel number 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-23T09:05:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q45",
      "57M25",
      "57R35",
      "57R70",
      "57R45"
    ],
    "keywords": [
      "morse-novikov number",
      "classical knot",
      "spun knot",
      "tunnel number"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}