{
  "id": "0709.1621",
  "version": "v2",
  "published": "2007-09-11T13:54:55.000Z",
  "updated": "2009-04-24T16:10:56.000Z",
  "title": "On the Configuration Spaces of Homogeneous Loop Quantum Cosmology and Loop Quantum Gravity",
  "authors": [
    "Johannes Brunnemann",
    "Christian Fleischhack"
  ],
  "comment": "12 pages, LaTeX. v1 to v2: Results unchanged. Presentation improved: Sect. 4 restructured (proof of Cor. 4.5 as well); some comments added; reference updated",
  "categories": [
    "math-ph",
    "gr-qc",
    "math.MP"
  ],
  "abstract": "The set of homogeneous isotropic connections, as used in loop quantum cosmology, forms a line $l$ in the space of all connections $\\cal A$. This embedding, however, does not continuously extend to an embedding of the configuration space $\\overline l$ of homogeneous isotropic loop quantum cosmology into that of loop quantum gravity, $\\overline{\\cal A}$. This follows from the fact that the parallel transports for general, non-straight paths in the base manifold do not depend almost periodically on $l$. Analogous results are given for the anisotropic case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-24T16:10:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C27",
      "53C05",
      "83F05"
    ],
    "keywords": [
      "homogeneous loop quantum cosmology",
      "loop quantum gravity",
      "configuration space",
      "homogeneous isotropic loop quantum cosmology",
      "connections"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 760520,
      "adsabs": "2007arXiv0709.1621B"
    }
  }
}