{
  "id": "1603.09110",
  "version": "v1",
  "published": "2016-03-30T10:23:34.000Z",
  "updated": "2016-03-30T10:23:34.000Z",
  "title": "Some spaces of polynomial knots",
  "authors": [
    "Hitesh Raundal",
    "Rama Mishra"
  ],
  "comment": "30 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we study the topology of three different kind of spaces associated to polynomial knots of degree at most $d$, for $d\\geq2$. We denote these spaces by $\\mathcal{O}_d$, $\\mathcal{P}_d$ and $\\mathcal{Q}_d$. For $d\\geq3$, we show that the spaces $\\mathcal{O}_d$ and $\\mathcal{P}_d$ are path connected and the space $\\mathcal{O}_d$ has homotopy type of $S^2$. Considering the space $\\mathcal{P}=\\bigcup_{d\\geq2}\\mathcal{O}_d$ of all polynomial knots with the inductive limit topology, we prove that it too has the same homotopy type as $S^2$. We also show that the number of path components of the space $\\mathcal{Q}_d$, for $d\\geq 2$, are in multiple of eight. Furthermore, we prove that the path components of the space $\\mathcal{Q}_d$ are contractible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-30T10:23:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P25",
      "57M25",
      "57M27",
      "57R40",
      "57R52"
    ],
    "keywords": [
      "polynomial knots",
      "path components",
      "homotopy type",
      "inductive limit topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160309110R"
    }
  }
}