{
  "id": "math/0209032",
  "version": "v2",
  "published": "2002-09-04T03:53:19.000Z",
  "updated": "2002-11-12T16:45:18.000Z",
  "title": "A K-theoretic refinement of topological realization of unstable algebras",
  "authors": [
    "Donald Yau"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "In this paper we propose and partially carry out a program to use $K$-theory to refine the topological realization problem of unstable algebras over the Steenrod algebra. In particular, we establish a suitable form of algebraic models for $K$-theory of spaces, called $\\psi^p$-algebras, which give rise to unstable algebras by taking associated graded algebras mod $p$. The aforementioned problem is then split into (i) the \\emph{algebraic} problem of realizing unstable algebras as mod $p$ associated graded of $\\psi^p$-algebras and (ii) the \\emph{topological} problem of realizing $\\psi^p$-algebras as $K$-theory of spaces. Regarding the algebraic problem, a theorem shows that every connected and even unstable algebra can be realized. We tackle the topological problem by obtaining a $K$-theoretic analogue of a theorem of Kuhn and Schwartz on the so-called Realization Conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-11-12T16:45:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55S10",
      "55S25"
    ],
    "keywords": [
      "unstable algebra",
      "k-theoretic refinement",
      "realization conjecture",
      "algebraic problem",
      "topological realization problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9032Y"
    }
  }
}