{
  "id": "1205.2858",
  "version": "v1",
  "published": "2012-05-13T13:34:06.000Z",
  "updated": "2012-05-13T13:34:06.000Z",
  "title": "Topological realizations and fundamental groups of higher-rank graphs",
  "authors": [
    "S. Kaliszewski",
    "Alex Kumjian",
    "John Quigg",
    "Aidan Sims"
  ],
  "comment": "23 pages; pictures prepared with TiKZ",
  "categories": [
    "math.CO",
    "math.OA"
  ],
  "abstract": "We investigate topological realizations of higher-rank graphs. We show that the fundamental group of a higher-rank graph coincides with the fundamental group of its topological realization. We also show that topological realization of higher-rank graphs is a functor, and that for each higher-rank graph \\Lambda, this functor determines a category equivalence between the category of coverings of \\Lambda\\ and the category of coverings of its topological realization. We discuss how topological realization relates to two standard constructions for k-graphs: projective limits and crossed products by finitely generated free abelian groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-13T13:34:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "14H30",
      "18D99"
    ],
    "keywords": [
      "fundamental group",
      "finitely generated free abelian groups",
      "higher-rank graph coincides",
      "standard constructions",
      "category equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.2858K"
    }
  }
}