{
  "id": "1902.01797",
  "version": "v1",
  "published": "2019-02-05T17:09:20.000Z",
  "updated": "2019-02-05T17:09:20.000Z",
  "title": "From Heegaard splittings to trisections; porting 3-dimensional ideas to dimension 4",
  "authors": [
    "David T. Gay"
  ],
  "comment": "28 pages, 9 figures, notes from mini-course at Winter Braids VIII, School on Braids and Low-dimensional Topology",
  "categories": [
    "math.GT"
  ],
  "abstract": "These notes summarize and expand on a mini-course given at CIRM in February 2018 as part of Winter Braids VIII. We somewhat obsessively develop the slogan `Trisections are to 4-manifolds as Heegaard splittings are to 3-manifolds', focusing on and clarifying the distinction between three ways of thinking of things: the basic definitions as decompositions of manifolds, the Morse theoretic perspective and descriptions in terms of diagrams. We also lay out these themes in two important relative settings: 4-manifolds with boundary and 4-manifolds with embedded 2-dimensional submanifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-05T17:09:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "57R45"
    ],
    "keywords": [
      "heegaard splittings",
      "trisections",
      "winter braids viii",
      "important relative settings",
      "basic definitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}