{
  "id": "1506.00084",
  "version": "v1",
  "published": "2015-05-30T07:22:38.000Z",
  "updated": "2015-05-30T07:22:38.000Z",
  "title": "Foundations of topological racks and quandles",
  "authors": [
    "Mohamed Elhamdadi",
    "El-kaïoum M. Moutuou"
  ],
  "comment": "Dedicated to Professor J\\'ozef H. Przytycki for his 60th birthday",
  "categories": [
    "math.GT",
    "math.AT",
    "math.QA",
    "math.RA"
  ],
  "abstract": "We give a foundational account on topological racks and quandles. Specifically, we define the notions of ideals, kernels, units, and inner automorphism group in the context of topological racks. Further, we investigate topological rack modules and principal rack bundles. Central extensions of topological racks are then introduced providing a first step towards a general continuous cohomology theory for topological racks and quandles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-30T07:22:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "20E22",
      "22E41"
    ],
    "keywords": [
      "foundations",
      "general continuous cohomology theory",
      "principal rack bundles",
      "inner automorphism group",
      "first step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150600084E"
    }
  }
}