{
  "id": "2005.06765",
  "version": "v1",
  "published": "2020-05-14T07:26:14.000Z",
  "updated": "2020-05-14T07:26:14.000Z",
  "title": "The maximum and minimum genus of a multibranched surface",
  "authors": [
    "Mario Eudave-Munoz",
    "Makoto Ozawa"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "In this paper, we give a lower bound for the maximum and minimum genus of a multibranched surface by the first Betti number and the minimum and maximum genus of the boundary of the neighborhood of it, respectively. As its application, we show that the maximum and minimum genus of $G\\times S^1$ is equal to twice of the maximum and minimum genus of $G$ for a graph $G$, respectively. This provides an interplay between graph theory and 3-manifold theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-14T07:26:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "minimum genus",
      "multibranched surface",
      "first betti number",
      "lower bound",
      "maximum genus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}