{
  "id": "1603.09041",
  "version": "v1",
  "published": "2016-03-30T05:16:17.000Z",
  "updated": "2016-03-30T05:16:17.000Z",
  "title": "Genera and minors of multibranched surfaces",
  "authors": [
    "Shosaku Matsuzaki",
    "Makoto Ozawa"
  ],
  "comment": "23 pages, 16 figures",
  "categories": [
    "math.GT",
    "math.AT",
    "math.CO"
  ],
  "abstract": "We say that a $2$-dimensional CW complex is a multibranched surface if we remove all points whose open neighborhoods are homeomorphic to the $2$-dimensional Euclidean space, then we obtain a $1$-dimensional complex which is homeomorphic to a disjoint union of some $S^1$'s. We define the genus of a multibranched surface $X$ as the minimum number of genera of $3$-dimensional manifold into which $X$ can be embedded. We prove some inequalities which give upper bounds for the genus of a multibranched surface. A multibranched surface is a generalization of graphs. Therefore, we can define \"minors\" of multibranched surfaces analogously. We study various properties of the minors of multibranched surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-30T05:16:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multibranched surface",
      "dimensional cw complex",
      "dimensional euclidean space",
      "upper bounds",
      "open neighborhoods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160309041M"
    }
  }
}