{
  "id": "math/0309106",
  "version": "v1",
  "published": "2003-09-05T19:00:39.000Z",
  "updated": "2003-09-05T19:00:39.000Z",
  "title": "Splitting With Continuous Control in Algebraic K-theory",
  "authors": [
    "David Rosenthal"
  ],
  "comment": "22 pages",
  "journal": "K-Theory 32 (2004), no. 2, 139--166",
  "categories": [
    "math.AT"
  ],
  "abstract": "In this work, the continuously controlled assembly map in algebraic $K$-theory, as developed by Carlsson and Pedersen, is proved to be a split injection for groups $\\Gamma$ that satisfy certain geometric conditions. The group $\\Gamma$ is allowed to have torsion, generalizing a result of Carlsson and Pedersen. Combining this with a result of John Moody, $K_0(k\\Gamma)$ is proved to be isomorphic to the colimit of $K_0(kH)$ over the finite subgroups $H$ of $\\Gamma$, when $\\Gamma$ is a virtually polycyclic group and $k$ is a field of characteristic zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-05T19:00:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18F25"
    ],
    "keywords": [
      "algebraic k-theory",
      "continuous control",
      "geometric conditions",
      "split injection",
      "john moody"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9106R"
    }
  }
}