{
  "id": "0908.2899",
  "version": "v2",
  "published": "2009-08-20T10:42:14.000Z",
  "updated": "2009-10-29T17:43:37.000Z",
  "title": "On Generalization of Homotopy of Words and Its Applications",
  "authors": [
    "Tomonori Fukunaga"
  ],
  "comment": "21 pages, 1 figure; We modified the definition of some invariants. See Remark 5.3",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "V. Turaev introduced the theory of topology of words and phrases in 2005. This is a combinatorialy extension of the theory of virtual knots and links. In this paper we generalize the notion of homotopy of words and phrases and we give geometric meanings of the generalized homotopy of words. Moreover using the generalized homotopy theory of words and phrases, we extend some homotopy invariants of nanophrases to $S$-homotopy invariant of nanowords with some homotopy data $S$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-29T17:43:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "68R15"
    ],
    "keywords": [
      "generalization",
      "applications",
      "homotopy invariant",
      "homotopy data",
      "generalized homotopy theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2899F"
    }
  }
}