{
  "id": "1803.00671",
  "version": "v1",
  "published": "2018-03-02T00:30:27.000Z",
  "updated": "2018-03-02T00:30:27.000Z",
  "title": "On the Classification of Topological Quandles",
  "authors": [
    "Zhiyun Cheng",
    "Mohamed Elhamdadi",
    "Boris Shekhtman"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We investigate the classification of topological quandles on some simple manifolds. Precisely we classify all Alexander quandle structures, up to isomorphism, on the real line and the unit circle. For the closed unit interval $[0, 1]$, we conjecture that there exists only one topological quandle structure on it, i.e. the trivial one. Some evidences are provided to support our conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-02T00:30:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classification",
      "alexander quandle structures",
      "simple manifolds",
      "unit circle",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}