{
  "id": "math/0210247",
  "version": "v1",
  "published": "2002-10-16T16:30:10.000Z",
  "updated": "2002-10-16T16:30:10.000Z",
  "title": "Cheeger manifolds and the classification of biquotients",
  "authors": [
    "Burt Totaro"
  ],
  "comment": "41 pages",
  "categories": [
    "math.DG",
    "math.AT"
  ],
  "abstract": "A closed manifold is called a biquotient if it is diffeomorphic to K\\G/H for some compact Lie group G with closed subgroups K and H such that K acts freely on G/H. Biquotients are a major source of examples of Riemannian manifolds with nonnegative sectional curvature. We prove several classification results for biquotients: (1) We classify all simply connected rational homology spheres which are diffeomorphic to biquotients. For example, the Gromoll-Meyer exotic sphere is the only exotic sphere of any dimension which is a biquotient. (2) We determine exactly which Cheeger manifolds, the connected sums of two rank-one symmetric spaces, are diffeomorphic to biquotients. For example, CP^2 # CP^2 is a biquotient, but CP^4 # HP^2 is not. (3) There are only finitely many diffeomorphism classes of 2-connected biquotients in each dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-16T16:30:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "57T15"
    ],
    "keywords": [
      "biquotient",
      "cheeger manifolds",
      "classification",
      "rank-one symmetric spaces",
      "compact lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10247T"
    }
  }
}