{
  "id": "0908.3580",
  "version": "v2",
  "published": "2009-08-25T09:33:38.000Z",
  "updated": "2009-10-24T04:42:59.000Z",
  "title": "On homotopy groups of the suspended classifying spaces",
  "authors": [
    "Roman Mikhailov",
    "Jie Wu"
  ],
  "comment": "Revised version, 46 pages",
  "journal": "Alg. Geom. Top. 10 (2010), 565-625",
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "In this paper, we determine the homotopy groups \\pi_4(\\Sigma K(A,1)) and \\pi_5(\\Sigma K(A,1)) for abelian groups A by using different facts and methods from group theory and homotopy theory: derived functors, the Carlsson simplicial construction, the Baues-Goerss spectral sequence, homotopy decompositions and the methods of algebraic K-theory. As the applications, we also determine \\pi_i(\\Sigma K(G,1)) with i=4,5 for some non-abelian groups G=\\Sigma_3 and SL(Z), and \\pi_4(\\Sigma K(A_4,1)) for the 4-th alternating group A_4.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-24T04:42:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q52",
      "55P20",
      "55P40",
      "55P65",
      "55Q35"
    ],
    "keywords": [
      "suspended classifying spaces",
      "homotopy groups",
      "baues-goerss spectral sequence",
      "carlsson simplicial construction",
      "algebraic k-theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.3580M"
    }
  }
}