{
  "id": "1702.05467",
  "version": "v1",
  "published": "2017-02-17T18:25:29.000Z",
  "updated": "2017-02-17T18:25:29.000Z",
  "title": "Smoothing closed gridded surfaces embedded in ${\\mathbb R}^4$",
  "authors": [
    "Juan Pablo Díaz",
    "Gabriela Hinojosa",
    "Rogelio Valdez",
    "Alberto Verjovsky"
  ],
  "comment": "8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We say that a topological $n$-manifold $N$ is a cubical $n$-manifold if it is contained in the $n$-skeleton of the canonical cubulation $\\mathcal{C}$ of ${\\mathbb{R}}^{n+k}$ ($k\\geq1$). In this paper, we prove that any closed, oriented cubical $2$-manifold has a transverse field of 2-planes in the sense of Whitehead and therefore it is smoothable by a small ambient isotopy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-17T18:25:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smoothing closed gridded surfaces",
      "small ambient isotopy",
      "transverse field",
      "canonical cubulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}