{
  "id": "1207.3373",
  "version": "v2",
  "published": "2012-07-13T22:37:11.000Z",
  "updated": "2013-05-11T15:13:09.000Z",
  "title": "A cohomology theory for colored tangles",
  "authors": [
    "Carmen Caprau"
  ],
  "comment": "13 pages, 4 figures; typos corrected and minor changes made to improve the exposition",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "We employ the sl(2) foam cohomology to define a cohomology theory for oriented framed tangles whose components are labelled by irreducible representations of U_q(sl(2)). We show that the corresponding colored invariants of tangles can be assembled into invariants of bigger tangles. For the case of knots and links, the corresponding theory is a categorification of the colored Jones polynomial, and provides a tool for efficient computations of the resulting colored invariant of knots and links. Our theory is defined over the Gaussian integers Z[i] (and more generally over Z[i][a,h], where a,h are formal parameters), and enhances the existing categorifications of the colored Jones polynomial.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-11T15:13:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "18G60"
    ],
    "keywords": [
      "cohomology theory",
      "colored tangles",
      "colored jones polynomial",
      "colored invariant",
      "foam cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1123027,
      "adsabs": "2012arXiv1207.3373C"
    }
  }
}