{
  "id": "math/0608517",
  "version": "v2",
  "published": "2006-08-21T16:26:36.000Z",
  "updated": "2009-03-30T20:31:18.000Z",
  "title": "The Heegaard genus of bundles over S^1",
  "authors": [
    "Mark Brittenham",
    "Yo'av Rieck"
  ],
  "comment": "This is the version published by Geometry & Topology Monographs on 3 December 2007",
  "journal": "Geom. Topol. Monogr. 12 (2007) 17-33",
  "doi": "10.2140/gtm.2007.12.17",
  "categories": [
    "math.GT"
  ],
  "abstract": "This paper explores connections between Heegaard genus, minimal surfaces, and pseudo-Anosov monodromies. Fixing a pseudo-Anosov map phi and an integer n, let M_n be the 3-manifold fibered over S^1 with monodromy phi^n. JH Rubinstein showed that for a large enough n every minimal surface of genus at most h in M_n is homotopic into a fiber; as a consequence Rubinstein concludes that every Heegaard surface of genus at most h for M_n is standard, that is, obtained by tubing together two fibers. We prove this result and also discuss related results of Lackenby and Souto.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-30T20:31:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57M10"
    ],
    "keywords": [
      "heegaard genus",
      "minimal surface",
      "pseudo-anosov map phi",
      "consequence rubinstein concludes",
      "pseudo-anosov monodromies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8517B"
    }
  }
}