{
  "id": "1902.06079",
  "version": "v1",
  "published": "2019-02-16T10:02:12.000Z",
  "updated": "2019-02-16T10:02:12.000Z",
  "title": "Classification of string links up to $2n$-moves and link-homotopy",
  "authors": [
    "Haruko A. Miyazawa",
    "Kodai Wada",
    "Akira Yasuhara"
  ],
  "comment": "16 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Two string links are equivalent up to $2n$-moves and link-homotopy if and only if their all Milnor link-homotopy invariants are congruent modulo $n$. Moreover, the set of the equivalence classes forms a finite group generated by elements of order $n$. The classification induces that if two string links are equivalent up to $2n$-moves for every $n>0$, then they are link-homotopic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-16T10:02:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "string links",
      "milnor link-homotopy invariants",
      "equivalence classes forms",
      "equivalent",
      "congruent modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}