{
  "id": "math/0306234",
  "version": "v1",
  "published": "2003-06-16T08:02:44.000Z",
  "updated": "2003-06-16T08:02:44.000Z",
  "title": "A finite loop space not rationally equivalent to a compact Lie group",
  "authors": [
    "Kasper K. S. Andersen",
    "Tilman Bauer",
    "Jesper Grodal",
    "Erik K. Pedersen"
  ],
  "comment": "8 pages",
  "journal": "Invent. Math 157 (2004), no. 1, 1--10.",
  "doi": "10.1007/s00222-003-0341-4",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact Lie group, extending the classical known bound of 5.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-16T08:02:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P35",
      "55P15",
      "55R35"
    ],
    "keywords": [
      "compact lie group",
      "rational cohomology",
      "connected finite loop space",
      "fact rationally equivalent",
      "counterexample"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2004,
      "month": "Jul",
      "volume": 157,
      "number": 1,
      "pages": 1
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004InMat.157....1A"
    }
  }
}