{
  "id": "0909.1434",
  "version": "v1",
  "published": "2009-09-08T09:16:41.000Z",
  "updated": "2009-09-08T09:16:41.000Z",
  "title": "Homotopy, Delta-equivalence and concordance for knots in the complement of a trivial link",
  "authors": [
    "Thomas Fleming",
    "Tetsuo Shibuya",
    "Tatsuya Tsukamoto",
    "Akira Yasuhara"
  ],
  "comment": "17 pages, 16 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Link-homotopy and self Delta-equivalence are equivalence relations on links. It was shown by J. Milnor (resp. the last author) that Milnor invariants determine whether or not a link is link-homotopic (resp. self Delta-equivalent) to a trivial link. We study link-homotopy and self Delta-equivalence on a certain component of a link with fixing the rest components, in other words, homotopy and Delta-equivalence of knots in the complement of a certain link. We show that Milnor invariants determine whether a knot in the complement of a trivial link is null-homotopic, and give a sufficient condition for such a knot to be Delta-equivalent to the trivial knot. We also give a sufficient condition for knots in the complements of the trivial knot to be equivalent up to Delta-equivalence and concordance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-08T09:16:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "trivial link",
      "complement",
      "milnor invariants determine",
      "concordance",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.1434F"
    }
  }
}