{
  "id": "0801.3294",
  "version": "v2",
  "published": "2008-01-22T00:46:52.000Z",
  "updated": "2008-11-20T00:05:46.000Z",
  "title": "A homology theory for Smale spaces: a summary",
  "authors": [
    "Ian F. Putnam"
  ],
  "comment": "Research summary; complete version in preparation. The new version gives a substantially simplified and more natural definition",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider Smale spaces, a particular class of hyperbolic topological dynamical systems, which include the basic sets for Smale's Axiom A systems. We present a homology theory for such systems which is based on the dimension group in the special case of shifts of finite type. This theory provides a Lefschetz formula relating trace data with the number of periodic points of the system.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-20T00:05:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C70",
      "37D20",
      "37B10"
    ],
    "keywords": [
      "smale spaces",
      "homology theory",
      "lefschetz formula relating trace data",
      "special case",
      "finite type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.3294P"
    }
  }
}