{
  "id": "2301.01121",
  "version": "v1",
  "published": "2023-01-03T14:36:56.000Z",
  "updated": "2023-01-03T14:36:56.000Z",
  "title": "The Euler characteristic of the moduli space of graphs",
  "authors": [
    "Michael Borinsky",
    "Karen Vogtmann"
  ],
  "comment": "40 pages",
  "categories": [
    "math.AT",
    "math-ph",
    "math.GR",
    "math.MP"
  ],
  "abstract": "The moduli space of rank $n$ graphs, the outer automorphism group of the free group of rank $n$ and Kontsevich's Lie graph complex have the same rational cohomology. We show that the associated Euler characteristic grows like $-e^{-1/4}\\,(n/e)^n/(n\\log n)^2$ as $n$ goes to infinity, and thereby prove that the total dimension of this cohomology grows rapidly with $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-03T14:36:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G85",
      "20F65",
      "20F28",
      "14T99",
      "20J06"
    ],
    "keywords": [
      "moduli space",
      "kontsevichs lie graph complex",
      "outer automorphism group",
      "associated euler characteristic grows",
      "free group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}