{
  "id": "0810.4183",
  "version": "v1",
  "published": "2008-10-22T23:48:05.000Z",
  "updated": "2008-10-22T23:48:05.000Z",
  "title": "On converting a side-pairing to a handle decomposition",
  "authors": [
    "Dubravko Ivanšić"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We give a method for obtaining a handle decomposition of an $n$-manifold if the manifold is given by isometric side-pairings of a polyhedron in $\\en$, $\\sn$ or $\\hn$. Every cycle of $k$-faces on the polyhedron corresponds to an $(n-k)$-handle of the manifold. Two applications of the method are given. One helps recognize when a noncompact hyperbolic 3-manifold is a complement of a link in $S^3$ (and automatically produces the link diagram), the other shows that a topological $S^4$ described by the author in \\cite{Ivansic3} is diffeomorphic to the standard differentiable $S^4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-22T23:48:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57M25",
      "57Q45"
    ],
    "keywords": [
      "handle decomposition",
      "isometric side-pairings",
      "polyhedron corresponds",
      "converting",
      "noncompact hyperbolic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.4183I"
    }
  }
}