{
  "id": "0809.4364",
  "version": "v1",
  "published": "2008-09-25T10:26:44.000Z",
  "updated": "2008-09-25T10:26:44.000Z",
  "title": "Moduli spaces of metric graphs of genus 1 with marks on vertices",
  "authors": [
    "Dmitry N. Kozlov"
  ],
  "comment": "Topology and its Applications, In Press, Corrected Proof, Available online 3 August 2008",
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "In this paper we study homotopy type of certain moduli spaces of metric graphs. More precisely, we show that the spaces $MG_{1,n}^v$, which parametrize the isometry classes of metric graphs of genus 1 with $n$ marks on vertices are homotopy equivalent to the spaces $TM_{1,n}$, which are the moduli spaces of tropical curves of genus 1 with $n$ marked points. Our proof proceeds by providing a sequence of explicit homotopies, with key role played by the so-called scanning homotopy. We conjecture that our result generalizes to the case of arbitrary genus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-25T10:26:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14Mxx"
    ],
    "keywords": [
      "moduli spaces",
      "metric graphs",
      "study homotopy type",
      "arbitrary genus",
      "result generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4364K"
    }
  }
}