{
  "id": "math/9903078",
  "version": "v1",
  "published": "1999-03-12T22:12:02.000Z",
  "updated": "1999-03-12T22:12:02.000Z",
  "title": "Annuli in generalized Heegaard splittings and degeneration of tunnel number",
  "authors": [
    "Martin Scharlemann",
    "Jennifer Schultens"
  ],
  "comment": "12 figures, 40 pages, including an appendix by Andrew Casson",
  "categories": [
    "math.GT"
  ],
  "abstract": "We analyze how a family of essential annuli in a compact 3-manifold will induce, from a strongly irreducible generalized Heegaard splitting of the ambient manifold, generalized Heegaard splittings of the complementary components. There are specific applications to the subadditivity of tunnel number of knots, improving somewhat bounds of Kowng. For example, in the absence of 2-bridge summands, the tunnel number of the sum of n knots is no less than 2/5 the sum of the tunnel numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-03-12T22:12:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M50",
      "57N10"
    ],
    "keywords": [
      "tunnel number",
      "irreducible generalized heegaard splitting",
      "degeneration",
      "complementary components",
      "ambient manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......3078S"
    }
  }
}