{
  "id": "0809.4940",
  "version": "v2",
  "published": "2008-09-29T11:35:00.000Z",
  "updated": "2009-11-27T18:42:58.000Z",
  "title": "Higher homotopy of groups definable in o-minimal structures",
  "authors": [
    "Alessandro Berarducci",
    "Marcello Mamino",
    "Margarita Otero"
  ],
  "comment": "13 pages, to be published in the Israel Journal of Mathematics",
  "categories": [
    "math.LO"
  ],
  "abstract": "It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups of G are isomorphic to the corresponding higher homotopy groups of L. As a consequence, we obtain that all abelian definably compact groups of a given dimension are definably homotopy equivalent, and that their universal cover are contractible.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-11-27T18:42:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "57T20",
      "55P45"
    ],
    "keywords": [
      "o-minimal structures",
      "groups definable",
      "o-minimal higher homotopy groups",
      "corresponding higher homotopy groups",
      "abelian definably compact groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4940B"
    }
  }
}