{
  "id": "1108.3055",
  "version": "v1",
  "published": "2011-08-15T18:50:24.000Z",
  "updated": "2011-08-15T18:50:24.000Z",
  "title": "A combinatorial description of homotopy groups of spheres",
  "authors": [
    "Roman Mikhailov",
    "Jie Wu"
  ],
  "comment": "27 pages, 1 figure",
  "categories": [
    "math.AT",
    "math.GR"
  ],
  "abstract": "We give a combinatorial description of general homotopy groups of $k$-dimensional spheres with $k\\geq3$ as well as those of Moore spaces. For $n>k\\geq 3,$ we construct a finitely generated group defined by explicit generators and relations, whose center is exactly $\\pi_n(S^k)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-15T18:50:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q40",
      "55Q20",
      "20F36"
    ],
    "keywords": [
      "combinatorial description",
      "general homotopy groups",
      "dimensional spheres",
      "moore spaces",
      "explicit generators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.3055M"
    }
  }
}