{
  "id": "0710.5926",
  "version": "v2",
  "published": "2007-10-31T18:47:58.000Z",
  "updated": "2021-05-10T05:11:10.000Z",
  "title": "Mod 2 cohomology of 2-local finite groups of low rank",
  "authors": [
    "Shizuo Kaji"
  ],
  "comment": "This is a revised version of \"Mod 2 cohomology of 2-compact groups of low rank\", J. of Math. of Kyoto Univ. 47 (2007), no. 2, 441--450",
  "journal": "J. of Math. of Kyoto Univ. 47 (2007), no. 2, 441--450",
  "doi": "10.1215/kjm/1250281055",
  "categories": [
    "math.AT",
    "math.GR"
  ],
  "abstract": "We determine the mod $2$ cohomology over the Steenrod algebra of the classifying spaces of the free loop groups $LG$ for compact groups $G=Spin(7)$, $Spin(8)$, $Spin(9)$, and $F_4$. Then, we show that they are isomorphic as algebras over the Steenrod algebra to the mod $2$ cohomology of the corresponding Chevalley groups of type $G(q)$, where $q$ is an odd prime power. In a similar manner, we compute the cohomology of the free loop space over $BDI(4)$ and show that it is isomorphic to that of $BSol(q)$ as algebras over the Steenrod algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-31T18:47:58.000Z",
      "abstract": "We determine the mod 2 cohomology over the Steenrod algebra of the classifying space of a free loop group LG for G=Spin(7), Spin(8), Spin(9), F_4, and DI(4). Then we show that it is isomorphic as algebras over the Steenrod algebra to the mod 2 cohomology of the classifying space of a certain 2-local finite group of type G.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2021-05-10T05:11:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R35",
      "55S10"
    ],
    "keywords": [
      "finite group",
      "low rank",
      "cohomology",
      "steenrod algebra",
      "free loop group lg"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.5926K"
    }
  }
}