{
  "id": "1712.02833",
  "version": "v1",
  "published": "2017-12-07T19:45:48.000Z",
  "updated": "2017-12-07T19:45:48.000Z",
  "title": "The covering type of closed surfaces and minimal triangulations",
  "authors": [
    "Eugenio Borghini",
    "Elias Gabriel Minian"
  ],
  "comment": "6 pages",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "The notion of covering type was recently introduced by Karoubi and Weibel to measure the complexity of a topological space by means of good coverings. When X has the homotopy type of a finite CW-complex, its covering type coincides with the minimum possible number of vertices of a simplicial complex homotopy equivalent to X. In this article we compute the covering type of all closed surfaces. Our results completely settle a problem posed by Karoubi and Weibel, and shed more light on the relationship between the topology of surfaces and the number of vertices of minimal triangulations from a homotopy point of view.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-07T19:45:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M20",
      "57Q15",
      "52B70",
      "57N16",
      "55M30",
      "55P15"
    ],
    "keywords": [
      "minimal triangulations",
      "closed surfaces",
      "simplicial complex homotopy equivalent",
      "homotopy point",
      "homotopy type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}