{
  "id": "0806.0637",
  "version": "v1",
  "published": "2008-06-03T21:12:02.000Z",
  "updated": "2008-06-03T21:12:02.000Z",
  "title": "On \"small geodesics\" and free loop spaces",
  "authors": [
    "A. Bahri",
    "F. R. Cohen"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "A topological group is constructed which is homotopy equivalent to the pointed loop space of a path-connected Riemannian manifold $M$ and which is given in terms of \"composable small geodesics\" on $M$. This model is analogous to J. Milnor's free group construction \\cite{Milnor} which provides a model for the pointed loop space of a connected simplicial complex. Related function spaces are constructed from \"composable small geodesics\" which provide models for the free loop space of $M$ as well as the space of continuous maps from a surface to $M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-03T21:12:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R99",
      "58D99"
    ],
    "keywords": [
      "free loop space",
      "composable small geodesics",
      "pointed loop space",
      "milnors free group construction",
      "riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.0637B"
    }
  }
}