{
  "id": "math/0606542",
  "version": "v3",
  "published": "2006-06-21T19:32:15.000Z",
  "updated": "2009-04-27T14:09:21.000Z",
  "title": "The Karoubi envelope and Lee's degeneration of Khovanov homology",
  "authors": [
    "Dror Bar-Natan",
    "Scott Morrison"
  ],
  "comment": "This is the version published by Algebraic & Geometric Topology on 4 October 2006",
  "journal": "Algebr. Geom. Topol. 6 (2006) 1459-1469",
  "doi": "10.2140/agt.2006.6.1459",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give a simple proof of Lee's result from [Adv. Math. 179 (2005) 554-586; arXiv:math.GT/0210213], that the dimension of the Lee variant of the Khovanov homology of a c-component link is 2^c, regardless of the number of crossings. Our method of proof is entirely local and hence we can state a Lee-type theorem for tangles as well as for knots and links. Our main tool is the \"Karoubi envelope of the cobordism category\", a certain enlargement of the cobordism category which is mild enough so that no information is lost yet strong enough to allow for some simplifications that are otherwise unavailable.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-04-27T14:09:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "18E05",
      "57M27"
    ],
    "keywords": [
      "khovanov homology",
      "karoubi envelope",
      "lees degeneration",
      "cobordism category",
      "simple proof"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6542B"
    }
  }
}