{
  "id": "0705.3453",
  "version": "v1",
  "published": "2007-05-23T19:50:53.000Z",
  "updated": "2007-05-23T19:50:53.000Z",
  "title": "Graphs on surfaces and Khovanov homology",
  "authors": [
    "Abhijit Champanerkar",
    "Ilya Kofman",
    "Neal Stoltzfus"
  ],
  "comment": "8 pages, 5 figures",
  "journal": "Algebraic and Geometric Topology 7 (2007), 1531-1540.",
  "categories": [
    "math.GT",
    "math.CO",
    "math.QA"
  ],
  "abstract": "Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We show that for any link diagram $L$, there is an associated ribbon graph whose quasi-trees correspond bijectively to spanning trees of the graph obtained by checkerboard coloring $L$. This correspondence preserves the bigrading used for the spanning tree model of Khovanov homology, whose Euler characteristic is the Jones polynomial of $L$. Thus, Khovanov homology can be expressed in terms of ribbon graphs, with generators given by ordered chord diagrams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-23T19:50:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M15",
      "05C10"
    ],
    "keywords": [
      "khovanov homology",
      "ordered chord diagram",
      "dessins denfant",
      "jones polynomial",
      "oriented ribbon graphs"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.3453C"
    }
  }
}