{
  "id": "2505.06887",
  "version": "v1",
  "published": "2025-05-11T07:50:21.000Z",
  "updated": "2025-05-11T07:50:21.000Z",
  "title": "Heegaard diagrams for $5$-manifolds",
  "authors": [
    "Geunyoung Kim"
  ],
  "comment": "32 pages, 19 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We introduce a version of Heegaard diagrams for $5$-dimensional cobordisms with $2$- and $3$-handles, $5$-dimensional $3$-handlebodies, and closed $5$-manifolds. We show that every such smooth $5$-manifold can be represented by a Heegaard diagram, and that two Heegaard diagrams represent diffeomorphic $5$-manifolds if and only if they are related by certain moves. As an application, we construct Heegaard diagrams for $5$-dimensional cobordisms from the standard $4$-sphere to the Gluck twists along knotted $2$-spheres. This provides several statements equivalent to the Gluck twist being diffeomorphic to the standard $4$-sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-11T07:50:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K40",
      "57K50",
      "57R65"
    ],
    "keywords": [
      "gluck twist",
      "dimensional cobordisms",
      "heegaard diagrams represent diffeomorphic",
      "construct heegaard diagrams",
      "statements equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}