{
  "id": "math/9903054",
  "version": "v2",
  "published": "1999-03-09T22:58:36.000Z",
  "updated": "1999-10-06T14:59:42.000Z",
  "title": "Solving the quintic by iteration in three dimensions",
  "authors": [
    "Scott Crass"
  ],
  "comment": "40 pages, 15 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S_5. Induced by its five-dimensional linear permutation representation is a three-dimensional projective action. A mapping of complex projective 3-space with this S_5 symmetry can provide the requisite symmetry-breaking tool. The article describes some of the S_5 geometry in CP^3 as well as several maps with particularly elegant geometric and dynamical properties. Using a rational map in degree six, it culminates with an explicit algorithm for solving a general quintic. In contrast to the Doyle-McMullen procedure - three 1-dimensional iterations, the present solution employs one 3-dimensional iteration.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-10-06T14:59:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensions",
      "five-dimensional linear permutation representation",
      "explicit algorithm",
      "requisite symmetry-breaking tool",
      "symmetric group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......3054C"
    }
  }
}