{
  "id": "0801.4218",
  "version": "v1",
  "published": "2008-01-28T09:26:53.000Z",
  "updated": "2008-01-28T09:26:53.000Z",
  "title": "Johnson's homomorphisms and the Arakelov-Green function",
  "authors": [
    "Nariya Kawazumi"
  ],
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "Let $\\pi: {\\mathbb C}_g \\to {\\mathbb M}_g$ be the universal family of compact Riemann surfaces of genus $g \\geq 1$. We introduce a real-valued function on the moduli space ${\\mathbb M}_g$ and compute the first and the second variations of the function. As a consequence we relate the Chern form of the relative tangent bundle $T_{{\\mathbb C}_g/{\\mathbb M}_g}$ induced by the Arakelov-Green function with differential forms on ${\\mathbb C}_g$ induced by a flat connection whose holonomy gives Johnson's homomorphisms on the mapping class group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-28T09:26:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R20",
      "14H15",
      "32G15"
    ],
    "keywords": [
      "arakelov-green function",
      "johnsons homomorphisms",
      "compact riemann surfaces",
      "moduli space",
      "relative tangent bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.4218K"
    }
  }
}