{
  "id": "1505.07629",
  "version": "v1",
  "published": "2015-05-28T10:21:00.000Z",
  "updated": "2015-05-28T10:21:00.000Z",
  "title": "Homotopy invariants of covers and KKM type lemmas",
  "authors": [
    "Oleg R. Musin"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AT",
    "math.CO",
    "math.GT"
  ],
  "abstract": "With any (open or closed) cover of a space T we associate certain homotopy classes of maps T into n-spheres. These homotopy invariants can be considered as obstructions for extensions of covers of a subspace A to a space X. We using these obstructions for generalizations of the classic KKM (Knaster-Kuratowski-Mazurkiewicz) and Sperner lemmas. In particular, we show that in the case when A is a k-sphere and X is a (k+1)-disk there exist KKM type lemmas for covers by n+2 sets if and only if the k-homotopy group of n-sphere is not zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-28T10:21:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kkm type lemmas",
      "homotopy invariants",
      "obstructions",
      "k-homotopy group",
      "homotopy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150507629M"
    }
  }
}