{
  "id": "math/0412271",
  "version": "v1",
  "published": "2004-12-14T07:48:11.000Z",
  "updated": "2004-12-14T07:48:11.000Z",
  "title": "An algebraic model for mod 2 topological cyclic homology",
  "authors": [
    "Kathryn Hess"
  ],
  "comment": "To appear in the CRM Lecture Notes from the Summer School on String Topology in Almeria, to be published by Birkhauser",
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "For any space X with the homotopy type of simply-connected, finite-type CW-complex, we construct an associative cochain algebra fls(X) whose cohomology algebra is isomorphic to that of LX, the free loop space on X. For certain X, we define a cochain map from fls(X) to itself that is a good model of the pth-power operation on LX. Under additional conditions on X, e.g., when X is a wedge of spheres, we define a cochain complex hos(X) by twisting together fls(X) and H*(BS^1) and prove that the cohomology of hos(X) is isomorphic to the Borel cohomology of LX. Finally, we define tc(X) to be the mapping cone of the composite of the projection map from hos(X) to fls(X) with the model of the pth-power map (for p=2), so that the mod 2 spectrum cohomology of TC(X;2), the topological cyclic homology of X at 2, is isomorphic to the mod 2 cohomology of tc(X). We conclude by calculating the mod 2 spectrum homology of TC(S^{2n+1}; 2).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-14T07:48:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P35",
      "18G55",
      "19D55",
      "55N91",
      "55P42",
      "55U10"
    ],
    "keywords": [
      "topological cyclic homology",
      "algebraic model",
      "cohomology",
      "cochain complex hos",
      "free loop space"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12271H"
    }
  }
}