{
  "id": "2203.10160",
  "version": "v1",
  "published": "2022-03-18T21:16:52.000Z",
  "updated": "2022-03-18T21:16:52.000Z",
  "title": "A Geometric Interpretation of Ranicki Duality",
  "authors": [
    "Frank Connolly"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Our main theorem provides an $(R,K)$ chain isomorphism: $ T\\Delta^*X\\cong C(X_K) $. Here $T$ is the Ranicki Duality functor; $\\Delta^*X$ is the simplicial cochain complex of the simplicial complex $X$, with control map $\\pi:X \\to K$ and $C(X_K) $ is the cellular chain complex of a CW complex $X_K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-18T21:16:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R67",
      "19J25"
    ],
    "keywords": [
      "geometric interpretation",
      "cellular chain complex",
      "ranicki duality functor",
      "simplicial cochain complex",
      "chain isomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}