{
  "id": "1703.10374",
  "version": "v1",
  "published": "2017-03-30T09:19:10.000Z",
  "updated": "2017-03-30T09:19:10.000Z",
  "title": "Fiber Strong Shape Theory for Topological Spaces",
  "authors": [
    "Vladimer Baladze",
    "Ruslan Tsinaridze"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "In the paper we construct and develop a fiber strong shape theory for arbitrary spaces over fixed metrizable space $\\Bo$. Our approach is based on the method of Marde\\v{s}i\\'{c}-Lisica and instead of resolutions, introduced by Marde\\v{s}i\\'{c}, their fiber preserving analogues are used. The fiber strong shape theory yields the classification of spaces over $\\Bo$ which is coarser than the classification of spaces over $\\Bo$ induced by fiber homotopy theory, but is finer than the classification of spaces over $\\Bo$ given by usual fiber shape theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-30T09:19:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C55",
      "54C56",
      "55P55"
    ],
    "keywords": [
      "topological spaces",
      "fiber strong shape theory yields",
      "usual fiber shape theory",
      "fiber homotopy theory",
      "classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}