{
  "id": "1708.04140",
  "version": "v1",
  "published": "2017-08-11T01:23:14.000Z",
  "updated": "2017-08-11T01:23:14.000Z",
  "title": "Morse functions to graphs and topological complexity for hyperbolic 3-manifolds",
  "authors": [
    "Diane Hoffoss",
    "Joseph Maher"
  ],
  "comment": "21 pages, 1 figure. arXiv admin note: text overlap with arXiv:1503.08521",
  "categories": [
    "math.GT"
  ],
  "abstract": "Scharlemann and Thompson define the width of a 3-manifold M as a notion of complexity based on the topology of M. Their original definition had the property that the adjacency relation on handles gave a linear order on handles, but here we consider a more general definition due to Saito, Scharlemann and Schultens, in which the adjacency relation on handles may give an arbitrary graph. We show that for compact hyperbolic 3-manifolds, this is linearly related to a notion of metric complexity, based on the areas of level sets of Morse functions to graphs, which we call Gromov area.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-11T01:23:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "morse functions",
      "topological complexity",
      "adjacency relation",
      "thompson define",
      "level sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}