{
  "id": "1703.05846",
  "version": "v1",
  "published": "2017-03-16T23:14:35.000Z",
  "updated": "2017-03-16T23:14:35.000Z",
  "title": "Trisecting Smooth 4-dimensional Cobordisms",
  "authors": [
    "Nickolas A. Castro"
  ],
  "comment": "19 pages, 11 Figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We extend the theory of relative trisections of smooth, compact, oriented $4$-manifolds with connected boundary given by Gay and Kirby to include $4$-manifolds with an arbitrary number of boundary components. Additionally, we provide sufficient conditions under which relatively trisected $4$-manifolds can be glued to one another along diffeomorphic boundary components so as to induce a trisected manifold. These two results allow us to define a category $\\textrm{Tri}$ whose objects are smooth, closed, oriented $3$-manifolds equipped with open book decompositions, and morphisms are relatively trisected cobordisms. Additionally, we extend the Hopf stabilization of open book decompositions to a relative stabilization of relative trisections.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-16T23:14:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99"
    ],
    "keywords": [
      "trisecting smooth",
      "open book decompositions",
      "cobordisms",
      "diffeomorphic boundary components",
      "relative trisections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}