{
  "id": "1807.10171",
  "version": "v1",
  "published": "2018-07-26T14:43:35.000Z",
  "updated": "2018-07-26T14:43:35.000Z",
  "title": "Section problems for configurations of points on the Riemann sphere",
  "authors": [
    "Lei Chen",
    "Nick Salter"
  ],
  "comment": "25 pages with 4 figures",
  "categories": [
    "math.GT",
    "math.AG",
    "math.GR"
  ],
  "abstract": "This paper contains a suite of results concerning the problem of adding $m$ distinct new points to a configuration of $n$ distinct points on the Riemann sphere, such that the new points depend continuously on the old. Altogether, the results of the paper provide a complete answer to the following question: given $n \\ne 5$, for which $m$ can one continuously add $m$ points to a configuration of $n$ points? For $n \\ge 6$, we find that $m$ must be divisible by $n(n-1)(n-2)$, and we provide a construction based on the idea of cabling of braids. For $n = 3,4$, we give some exceptional constructions based on the theory of elliptic curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-26T14:43:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann sphere",
      "section problems",
      "configuration",
      "elliptic curves",
      "paper contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}