{
  "id": "1302.0507",
  "version": "v4",
  "published": "2013-02-03T16:30:25.000Z",
  "updated": "2014-09-23T15:55:27.000Z",
  "title": "Group actions on Spheres with rank one isotropy",
  "authors": [
    "Ian Hambleton",
    "Ergun Yalcin"
  ],
  "comment": "22 pages. Trans. Amer. Math. Soc. (to appear); sequel to \"Homotopy Representations over the Orbit Category\", Homology, Homotopy and Applications (arXiv:1402.3306)",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Let G be a rank two finite group, and let $\\cH$ denote the family of rank one p-subgroups of G, at all primes where G has p-rank two. We show that a rank two finite group G which satisfies certain group-theoretic conditions admits a finite G-CW-complex X with isotropy in $\\cH$, whose fixed sets are homotopy spheres. Our construction provides an infinite family of new non-linear G-CW-complex examples for many of the rank two finite simple groups.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-19T16:13:10.000Z",
      "abstract": "Let G be a rank two finite group, and let $\\cH$ denote the family of rank one p-subgroups of G, at all primes where G has p-rank two. We show that a rank two finite group G which satisfies certain group-theoretic conditions admits a finite G-CW-complex X with isotropy in $\\cH$, whose fixed sets are homotopy spheres. Our construction provides an infinite family of new examples.",
      "comment": "22 pages. This is the second part of a new two-part revision of this work. Some foundational results have been moved to the first part: \"Homotopy Representations over the Orbit Category\" (arXiv:1402.3306). In the new part two, we have improved the exposition and constructed non-linear G-CW complex examples for most of the finite simple groups G of rank two",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-09-23T15:55:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S17",
      "55U15",
      "20J05",
      "18Gxx"
    ],
    "keywords": [
      "group actions",
      "finite group",
      "group-theoretic conditions admits",
      "finite g-cw-complex",
      "homotopy spheres"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.0507H"
    }
  }
}