{
  "id": "math/0702165",
  "version": "v2",
  "published": "2007-02-07T01:05:40.000Z",
  "updated": "2007-08-24T19:52:34.000Z",
  "title": "Graph homology of moduli space of pointed real curves of genus zero",
  "authors": [
    "Ozgur Ceyhan"
  ],
  "comment": "38 pages, 4 figures. To appear in Selecta Mathematica",
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "The moduli space $\\bar{M}_S^\\sigma(R)$ parameterizes the isomorphism classes of $S$-pointed stable real curves of genus zero which are invariant under relabeling by the involution $\\sigma$. This moduli space is stratified according to the degeneration types of $\\sigma$-invariant curves. The degeneration types of $\\sigma$-invariant curves are encoded by their dual trees with additional decorations. We construct a combinatorial graph complex generated by the fundamental classes of strata of $\\bar{M}_S^\\sigma(R)$. We show that the homology of $\\bar{M}_S^\\sigma(R)$ is isomorphic to the homology of our graph complex. We also give a presentation of the fundamental group of $\\bar{M}_S^\\sigma(R)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-24T19:52:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "pointed real curves",
      "genus zero",
      "graph homology",
      "degeneration types"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2165C"
    }
  }
}