{
  "id": "2109.09196",
  "version": "v1",
  "published": "2021-09-19T19:12:01.000Z",
  "updated": "2021-09-19T19:12:01.000Z",
  "title": "Symmetries of exotic smoothings of aspherical space forms",
  "authors": [
    "Mauricio Bustamante",
    "Bena Tshishiku"
  ],
  "comment": "19 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study finite group actions on smooth manifolds of the form $W\\#\\Sigma$, where $\\Sigma$ is an exotic $n$-sphere and $W$ is either a hyperbolic or a flat manifold. In the flat case, we classify the finite cyclic groups that act freely on an exotic torus $T^n\\#\\Sigma$. For hyperbolic manifolds $M$, we produce examples $M\\#\\Sigma$ that admit no nontrivial smooth action of a finite group, while Isom($M$) is arbitrarily large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-19T19:12:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R55",
      "57S17",
      "57R60",
      "22F30"
    ],
    "keywords": [
      "aspherical space forms",
      "exotic smoothings",
      "study finite group actions",
      "symmetries",
      "finite cyclic groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}