{
  "id": "1503.06504",
  "version": "v1",
  "published": "2015-03-23T01:29:41.000Z",
  "updated": "2015-03-23T01:29:41.000Z",
  "title": "Coassembly and the $K$-theory of finite groups",
  "authors": [
    "Cary Malkiewich"
  ],
  "comment": "49 pages",
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "We study the $K$-theory and Swan theory of the group ring $R[G]$, when $G$ is a finite group and $R$ is any discrete ring or ring spectrum. In this setting, the well-known assembly map for $K(R[G])$ has a lesser-known companion called the coassembly map. We prove that their composite is the equivariant norm of $K(R)$. As a result, we get a splitting of both assembly and coassembly after $K(n)$-localization, and an apparently new map from the Whitehead torsion group of $G$ over $R$ to the Tate cohomology of $BG$ with coefficients in $K(R)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-23T01:29:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18F25",
      "19D10",
      "55R12",
      "55R70"
    ],
    "keywords": [
      "finite group",
      "whitehead torsion group",
      "tate cohomology",
      "equivariant norm",
      "swan theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150306504M"
    }
  }
}