{
  "id": "1602.01386",
  "version": "v1",
  "published": "2016-02-03T17:39:03.000Z",
  "updated": "2016-02-03T17:39:03.000Z",
  "title": "A Khovanov stable homotopy type for colored links",
  "authors": [
    "Andrew Lobb",
    "Patrick Orson",
    "Dirk Schuetz"
  ],
  "comment": "16 pages, 6 figures",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We extend Lipshitz-Sarkar's definition of a stable homotopy type associated to a link L whose cohomology recovers the Khovanov cohomology of L. Given an assignment c (called a coloring) of positive integer to each component of a link L, we define a stable homotopy type X_col(L_c) whose cohomology recovers the c-colored Khovanov cohomology of L. This goes via Rozansky's definition of a categorified Jones-Wenzl projector P_n as an infinite torus braid on n strands. We then observe that Cooper-Krushkal's explicit definition of P_2 also gives rise to stable homotopy types of colored links (using the restricted palette {1, 2}), and we show that these coincide with X_col. We use this equivalence to compute the stable homotopy type of the (2,1)-colored Hopf link and the 2-colored trefoil. Finally, we discuss the Cooper-Krushkal projector P_3 and make a conjecture of X_col(U_3) for U the unknot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-03T17:39:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "khovanov stable homotopy type",
      "colored links",
      "khovanov cohomology",
      "extend lipshitz-sarkars definition",
      "cooper-krushkals explicit definition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160201386L"
    }
  }
}