{
  "id": "1604.03067",
  "version": "v1",
  "published": "2016-04-11T18:57:35.000Z",
  "updated": "2016-04-11T18:57:35.000Z",
  "title": "The transfer map of free loop spaces",
  "authors": [
    "John A. Lind",
    "Cary Malkiewich"
  ],
  "comment": "49 pages, 6 figures",
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "For any perfect fibration $E \\rightarrow B$, there is a \"free loop transfer map\" $LB_+ \\rightarrow LE_+$, defined using topological Hochschild homology. We prove that this transfer is compatible with the Becker-Gottlieb transfer, allowing us to extend a result of Dorabia\\l{}a and Johnson on the transfer map in Waldhausen's $A$-theory. In the case where $E \\rightarrow B$ is a smooth fiber bundle, we also give a concrete geometric model for the free loop transfer in terms of Pontryagin-Thom collapse maps. We recover the previously known computations of the free loop transfer due to Schlichtkrull, and make a few new computations as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-11T18:57:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R12",
      "19D55",
      "16E40",
      "55M05"
    ],
    "keywords": [
      "free loop spaces",
      "free loop transfer map",
      "smooth fiber bundle",
      "concrete geometric model",
      "pontryagin-thom collapse maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}