{
  "id": "math/0202042",
  "version": "v1",
  "published": "2002-02-05T19:20:30.000Z",
  "updated": "2002-02-05T19:20:30.000Z",
  "title": "The McCord model for the tensor product of a space and a commutative ring spectrum",
  "authors": [
    "Nicholas J. Kuhn"
  ],
  "comment": "AMSLatex with xypics. 22 pages",
  "categories": [
    "math.AT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "This paper begins by noting that, in a 1969 paper in the Transactions, M.C.McCord introduced a construction that can be interpreted as a model for the categorical tensor product of a based space and a topological abelian group. This can be adapted to Segal's very special Gamma--spaces, and then to a more modern situation: (K tensor R) where K is a based space and R is a unital, augmented, commutative, associative S--algebra. The model comes with an easy-to-describe filtration. If one lets K = S^n, and then stabilize with respect to n, one gets a filtered model for the Topological Andre--Quillen Homology of R. When R = Omega^{infty} Sigma^{infty} X, one arrives at a filtered model for the connective cover of a spectrum X, constructed from its 0th space. Another example comes by letting K be a finite complex, and R the S--dual of a finite complex Z. Dualizing again, one arrives at G.Arone's model for the Goodwillie tower of the functor sending Z to the suspension spectrum of Map(K,Z). Applying cohomology with field coefficients, one gets various spectral sequences for deloopings with known E_1--terms. A few nontrivial examples are given. In an appendix, we describe the construction for unital, commutative, associative S--algebras not necessarily augmented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-05T19:20:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P43",
      "18G55"
    ],
    "keywords": [
      "tensor product",
      "commutative ring spectrum",
      "mccord model",
      "finite complex",
      "associative s-algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2042K"
    }
  }
}