{
  "id": "1802.01757",
  "version": "v1",
  "published": "2018-02-06T01:45:03.000Z",
  "updated": "2018-02-06T01:45:03.000Z",
  "title": "Topological symmetries of simply-connected four-manifolds and actions of automorphism groups of free groups",
  "authors": [
    "Shengkui Ye"
  ],
  "categories": [
    "math.GT",
    "math.AT",
    "math.DS"
  ],
  "abstract": "Let $M$ be a simply connected closed $4$-manifold. It is proved that any (possibly finite) compact Lie group acting effectively and homologically trivially on $M$ by homeomorphisms is an abelian group of rank at most two. As applications, let $\\mathrm{Aut}(F_{n})$ be the automorphism group of the free group of rank $n.$ We prove that any group action of $\\mathrm{Aut}% (F_{n})$ $(n\\geq 4)$ on $M\\neq S^{4}$ by homologically trivial homeomorphisms factors through $\\mathbb{Z}/2.$ Moreover, any action of $% \\mathrm{SL}_{n}(\\mathbb{Q})$ $(n\\geq 4)$ on $M\\neq S^{4}$ by homeomorphisms is trivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-06T01:45:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free group",
      "automorphism group",
      "simply-connected four-manifolds",
      "topological symmetries",
      "homologically trivial homeomorphisms factors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}