{
  "id": "1502.07611",
  "version": "v1",
  "published": "2015-02-26T16:00:55.000Z",
  "updated": "2015-02-26T16:00:55.000Z",
  "title": "The slice spectral sequence for the $C_{4}$ analog of real $K$-theory",
  "authors": [
    "M. A. Hill",
    "M. J. Hopkins",
    "D. C. Ravenel"
  ],
  "comment": "68 pages, 4 tables and 17 figures",
  "categories": [
    "math.AT"
  ],
  "abstract": "We describe the slice spectral sequence of a 32-periodic $C_{4}$-spectrum $K_{\\bf H}$ related to the $C_{4}$ norm ${N_{C_{2}}^{C_{4}}MU_{\\bf R}}$ of the real cobordism spectrum $MU_{\\bf R}$. We will give it as a spectral sequence of Mackey functors converging to the graded Mackey functor $\\underline{\\pi }_{*}K_{\\bf H}$, complete with differentials and exotic extensions in the Mackey functor structure. The slice spectral sequence for the 8-periodic real $K$-theory spectrum $K_{\\bf R}$ was first analyzed by Dugger. The $C_{8}$ analog of $K_{\\bf H}$ is 256-periodic and detects the Kervaire invariant classes $\\theta_{j}$. A partial analysis of its slice spectral sequence led to the solution to the Kervaire invariant problem, namely the theorem that $\\theta_{j}$ does not exist for $j\\geq 7$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-26T16:00:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q10",
      "55Q91",
      "55P42",
      "55R45",
      "55T99"
    ],
    "keywords": [
      "slice spectral sequence",
      "kervaire invariant classes",
      "mackey functor structure",
      "kervaire invariant problem",
      "real cobordism spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 68,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150207611H"
    }
  }
}