{
  "id": "0808.1686",
  "version": "v2",
  "published": "2008-08-12T15:46:44.000Z",
  "updated": "2010-08-26T15:24:11.000Z",
  "title": "Bundles of coloured posets and a Leray-Serre spectral sequence for Khovanov homology",
  "authors": [
    "Brent Everitt",
    "Paul Turner"
  ],
  "comment": "22 pages; minor changes since version 1, including the addition of the words, \"for Khovanov homology\" to the end of the title",
  "journal": "Trans. Amer. Math. Soc., 364 (6), 2012, 3137-3158",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "The decorated hypercube found in the construction of Khovanov homology for links is an example of a Boolean lattice equipped with a presheaf of modules. One can place this in a wider setting as an example of a coloured poset, that is to say a poset with a unique maximal element equipped with a presheaf of modules. In this paper we initiate the study of a bundle theory for coloured posets, producing for a certain class of base posets a Leray-Serre type spectral sequence. We then show how this theory finds application in Khovanov homology by producing a new spectral sequence converging to the Khovanov homology of a given link.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-26T15:24:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "khovanov homology",
      "leray-serre spectral sequence",
      "coloured poset",
      "leray-serre type spectral sequence",
      "unique maximal element"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.1686E"
    }
  }
}