{
  "id": "0906.0220",
  "version": "v3",
  "published": "2009-06-01T07:52:16.000Z",
  "updated": "2009-10-29T18:03:46.000Z",
  "title": "Quantum (sl_n, \\land V_n) link invariant and matrix factorizations",
  "authors": [
    "Yasuyoshi Yonezawa"
  ],
  "comment": "Doctoral thesis (October, Nagoya University)",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "M. Khovanov and L. Rozansky gave a categorification of the HOMFLY-PT polynomial. This study is a generalization of the Khovanov-Rozansky homology. We define a homology associated to the quantum $(sl_n,\\land V_n)$ link invariant, where $\\land V_n$ is the set of the fundamental representations of the quantum group of $sl_n$. In the case of a [1,k]-colored link diagram, we prove that its homology is a link invariant. In the case of an [i,j]-colored link diagram, we define a normalized Poincare polynomial of its homology and prove the polynomial is a link invariant.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-10-29T18:03:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "link invariant",
      "matrix factorizations",
      "link diagram",
      "quantum group",
      "homfly-pt polynomial"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.0220Y"
    }
  }
}