{
  "id": "1610.06373",
  "version": "v1",
  "published": "2016-10-20T12:07:37.000Z",
  "updated": "2016-10-20T12:07:37.000Z",
  "title": "Diagrams for Relative Trisections",
  "authors": [
    "Nickolas A. Castro",
    "David T. Gay",
    "Juanita Pinzon-Caicedo"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We establish a correspondence between trisections of smooth, compact, oriented $4$--manifolds with connected boundary and diagrams describing these trisected $4$--manifolds. Such a diagram comes in the form of a compact, oriented surface with boundary together with three tuples of simple closed curves, with possibly fewer curves than the genus of the surface, satisfying a pairwise standardness condition. This should be thought of as the $4$--dimensional analog of a sutured Heegaard diagram for a sutured $3$--manifold. We also give many foundational examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-20T12:07:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "relative trisections",
      "possibly fewer curves",
      "foundational examples",
      "diagram comes",
      "sutured heegaard diagram"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}