{
  "id": "math/0502402",
  "version": "v2",
  "published": "2005-02-18T18:12:18.000Z",
  "updated": "2005-04-19T20:26:04.000Z",
  "title": "Topological fundamental groups can distinguish spaces with isomorphic homotopy groups",
  "authors": [
    "Paul Fabel"
  ],
  "comment": "5 pages; minor improvements",
  "categories": [
    "math.AT",
    "math.GN"
  ],
  "abstract": "We exhibit a map f between aspherical spaces X and Y such that f induces an isomorphism on homotopy groups but, with natural topologies, X and Y fail to have homeomorphic fundamental groups. Thus the topological fundamental group has the capacity to distinguish homotopy type when the Whitehead theorem fails.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-04-19T20:26:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P15"
    ],
    "keywords": [
      "topological fundamental group",
      "isomorphic homotopy groups",
      "distinguish spaces",
      "whitehead theorem fails",
      "homeomorphic fundamental groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2402F"
    }
  }
}