{
  "id": "1610.04092",
  "version": "v1",
  "published": "2016-10-13T14:11:12.000Z",
  "updated": "2016-10-13T14:11:12.000Z",
  "title": "A new algorith for 3-sphere recognition",
  "authors": [
    "Michael Heusener",
    "Raphael Zentner"
  ],
  "comment": "8 pages, comments are welcome",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We prove the existence of a new algorithm for 3-sphere recognition based on Groebner basis methods applied to the variety of $\\text{\\em SL}(2,\\C)$-representation of the fundamental group. An essential input is a recent result of the second author, stating that any integer homology 3-sphere different from the 3-sphere admits an irreducible representation of its fundamental group in $\\text{\\em SL}(2,\\C)$. This result, and hence our algorithm, build on the geometrisation theorem of 3-manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-13T14:11:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "recognition",
      "fundamental group",
      "groebner basis methods",
      "geometrisation theorem",
      "representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}