{
  "id": "1510.05419",
  "version": "v1",
  "published": "2015-10-19T10:59:27.000Z",
  "updated": "2015-10-19T10:59:27.000Z",
  "title": "Shellability and Sphericity of the quasi-arc complex of the Möbius strip",
  "authors": [
    "Jon Wilson"
  ],
  "comment": "33 pages, 35 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Shellability of a simplicial complex has many useful structural implications. In particular, it was shown by Danaraj and Klee that every shellable pseudo-manifold is a PL-sphere. The purpose of this paper is to prove the shellability of the quasi-arc complex of the M\\\"obius strip. Along the way we provide elementary proofs of the shellability of the arc complex of the $n$-gon and the cylinder. In turn, applying the result of Danaraj and Klee, we obtain the sphericity of all of these complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-19T10:59:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasi-arc complex",
      "möbius strip",
      "shellability",
      "sphericity",
      "simplicial complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151005419W"
    }
  }
}