{
  "id": "math/0405079",
  "version": "v1",
  "published": "2004-05-05T15:05:22.000Z",
  "updated": "2004-05-05T15:05:22.000Z",
  "title": "Units of ring spectra and their traces in algebraic K-theory",
  "authors": [
    "Christian Schlichtkrull"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper16.abs.html",
  "journal": "Geom. Topol. 8(2004) 645-673",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let GL_1(R) be the units of a commutative ring spectrum R. In this paper we identify the composition BGL_1(R)->K(R)->THH(R)->\\Omega^{\\infty}(R), where K(R) is the algebraic K-theory and THH(R) the topological Hochschild homology of R. As a corollary we show that classes in \\pi_{i-1}(R) not annihilated by the stable Hopf map give rise to non-trivial classes in K_i(R) for i\\geq 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-05T15:05:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19D55",
      "55P43",
      "19D10",
      "55P48"
    ],
    "keywords": [
      "algebraic k-theory",
      "stable hopf map",
      "non-trivial classes",
      "topological hochschild homology",
      "composition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}