{
  "id": "math/0609516",
  "version": "v1",
  "published": "2006-09-19T06:12:08.000Z",
  "updated": "2006-09-19T06:12:08.000Z",
  "title": "Lectures on Topology of Words",
  "authors": [
    "Vladimir Turaev"
  ],
  "comment": "40 pages, lecture notes for a series of lectures given in RIMS, Kyoto University in February 2006",
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "We discuss a topological approach to words introduced by the author. Words on an arbitrary alphabet are approximated by Gauss words and then studied up to natural modifications inspired by the Reidemeister moves on knot diagrams. This leads us to a notion of homotopy for words. We introduce several homotopy invariants of words and give a homotopy classification of words of length five.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-19T06:12:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "57M99"
    ],
    "keywords": [
      "gauss words",
      "arbitrary alphabet",
      "reidemeister moves",
      "knot diagrams",
      "homotopy invariants"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9516T"
    }
  }
}