{
  "id": "math/0502195",
  "version": "v2",
  "published": "2005-02-09T16:09:10.000Z",
  "updated": "2005-10-17T17:09:15.000Z",
  "title": "Hopf algebra structure on topological Hochschild homology",
  "authors": [
    "Vigleik Angeltveit",
    "John Rognes"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-49.abs.html",
  "journal": "Algebr. Geom. Topol. 5 (2005) 1223-1290",
  "categories": [
    "math.AT"
  ],
  "abstract": "The topological Hochschild homology THH(R) of a commutative S-algebra (E_infty ring spectrum) R naturally has the structure of a commutative R-algebra in the strict sense, and of a Hopf algebra over R in the homotopy category. We show, under a flatness assumption, that this makes the Boekstedt spectral sequence converging to the mod p homology of THH(R) into a Hopf algebra spectral sequence. We then apply this additional structure to the study of some interesting examples, including the commutative S-algebras ku, ko, tmf, ju and j, and to calculate the homotopy groups of THH(ku) and THH(ko) after smashing with suitable finite complexes. This is part of a program to make systematic computations of the algebraic K-theory of S-algebras, by means of the cyclotomic trace map to topological cyclic homology.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-10-17T17:09:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P43",
      "55S10",
      "55S12",
      "57T05",
      "13D03",
      "55T15"
    ],
    "keywords": [
      "hopf algebra structure",
      "hopf algebra spectral sequence",
      "commutative s-algebra",
      "topological hochschild homology thh",
      "cyclotomic trace map"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2195A"
    }
  }
}