{
  "id": "1801.06585",
  "version": "v1",
  "published": "2018-01-19T21:53:20.000Z",
  "updated": "2018-01-19T21:53:20.000Z",
  "title": "On two types of $Z$-monodromy in triangulations of surfaces",
  "authors": [
    "Mark Pankov",
    "Adam Tyc"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\Gamma$ be a triangulation of a connected closed $2$-dimensional (not necessarily orientable) surface. Using zigzags (closed left-right paths), for every face of $\\Gamma$ we define the $z$-monodromy which acts on the oriented edges of this face. There are precisely $7$ types of $z$-monodromies. We consider the following two cases: (M1) the $z$-monodromy is identity, (M2) the $z$-monodromy is the consecutive passing of the oriented edges. Our main result is the following: the subgraphs of the dual graph $\\Gamma^{*}$ formed by edges whose $z$-monodromies are of types (M1) and (M2), respectively, both are forests.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-19T21:53:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triangulation",
      "oriented edges",
      "closed left-right paths",
      "main result",
      "dual graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}