{
  "id": "1001.0618",
  "version": "v1",
  "published": "2010-01-05T03:12:42.000Z",
  "updated": "2010-01-05T03:12:42.000Z",
  "title": "The Laplace transform of the cut-and-join equation of Mariño-Vafa formula and its applications",
  "authors": [
    "Shengmao Zhu"
  ],
  "comment": "48 pages",
  "categories": [
    "math.AG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "By the same method introduced in [9], we calculate the Laplace transform of the celebrated cut-and-join equation of Mari\\~no-Vafa formula discovered by C. Liu, K. Liu and J. Zhou [17]. Then, we study the applications of the polynomial identity (1) obtained in theorem 1.1 of this paper. We show the proof Bouchard-Mari\\~no conjecture for C^3 which was given by L. Chen [5] Firstly. Subsequently, we will present how to obtain series Hodge integral identities from this polynomial identity (1). In particular, the main result in [9] is one of special case in such series of Hodge integral identities. At last, we give a explicit formula for the computation of Hodge integral <\\tau_{b_L}\\lamda_{g}\\lamda_{1}>_{g} where b_L = (b_1,..,b_l).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-05T03:12:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14N10",
      "14N35",
      "05A15",
      "05A17",
      "81T45"
    ],
    "keywords": [
      "laplace transform",
      "mariño-vafa formula",
      "applications",
      "polynomial identity",
      "series hodge integral identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.0618Z"
    }
  }
}