{
  "id": "0903.2248",
  "version": "v1",
  "published": "2009-03-12T18:39:43.000Z",
  "updated": "2009-03-12T18:39:43.000Z",
  "title": "On the Taylor Tower of Relative K-theory",
  "authors": [
    "Ayelet Lindenstrauss",
    "Randy McCarthy"
  ],
  "comment": "66 pages, plain tex",
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "For a functor with smash product F and an F-bimodule P, we construct an invariant W(F;P) which is an analog of TR(F) with coefficients. We study the structure of this invariant and its finite-stage approximations W_n(F;P), and conclude that for F the FSP associated to a ring R and P the FSP associated to the simplicial R-bimodule M[X] (with M a simplicial R-bimodule, X a simplicial set), the functor sending X to W_n(R;M[X]) is the nth stage of the Goodwillie calculus Taylor tower of the functor which sends X to the reduced K-theory spectrum of R with coefficients in M[X]. Thus the functor sending X to W(R;M[X]) is the full Taylor tower, which converges to the reduced K-theory of R with coefficients in M[X] for connected X. We show the equivalence between relative K-theory of R with coefficients in M[-] and W(R;M[-]) using Goodwillie calculus: we construct a natural transformation between the two functors, both of which are 0-analytic, and show that this natural transformation induces an equivalence on the derivatives at any connected X.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-12T18:39:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19D55",
      "55P91",
      "18G60"
    ],
    "keywords": [
      "relative k-theory",
      "coefficients",
      "simplicial r-bimodule",
      "goodwillie calculus taylor tower",
      "reduced k-theory"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 66,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2248L"
    }
  }
}