{
  "id": "1008.4443",
  "version": "v3",
  "published": "2010-08-26T07:12:22.000Z",
  "updated": "2017-05-10T13:57:47.000Z",
  "title": "Spectral sequences of colored Jones polynomials, colored Rasmussen invariants and nanophrases",
  "authors": [
    "Noboru Ito"
  ],
  "comment": "This manuscript depends on arXiv: 1008.0956 which was withdrawn. Therefore, so it is with this manuscript",
  "categories": [
    "math.GT",
    "math.CO",
    "math.QA"
  ],
  "abstract": "We introduce three spectral sequences which give some expressions of colored Jones polynomials. Each spectral sequence contains a Khovanov-type homology groups. Two of them are derived from a bicomplex of the colored Jones polynomial. The other is the spectral sequence that deduces a colored Rasmussen invariant of links. We also introduce three functors between categories of nanophrases, generalizations of links, and obtain their applications using colored Jones polynomials and their categorifications.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-24T09:46:52.000Z",
      "comment": "8 pages. Second version: minor changes",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-05-10T13:57:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "68R15"
    ],
    "keywords": [
      "colored jones polynomial",
      "colored rasmussen invariant",
      "nanophrases",
      "khovanov-type homology groups",
      "spectral sequence contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.4443I"
    }
  }
}