{
  "id": "1412.4572",
  "version": "v1",
  "published": "2014-12-15T13:02:18.000Z",
  "updated": "2014-12-15T13:02:18.000Z",
  "title": "The large scale geometry of strongly aperiodic subshifts of finite type",
  "authors": [
    "David Bruce Cohen"
  ],
  "comment": "28 pages, 6 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "A subshift on a group G is a closed, G-invariant subset of A^G, for some finite set A. It is said to be of finite type if it is defined by a finite collection of \"forbidden patterns\" and to be strongly aperiodic if it has no points fixed by a nontrivial element of the group. We show that if G has at least two ends, then there are no strongly aperiodic subshifts of finite type on G (as was previously known for free groups). Additionally, we show that among torsion free, finitely presented groups, the property of having a strongly aperiodic subshift of finite type is invariant under quasi isometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-15T13:02:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "37B10"
    ],
    "keywords": [
      "strongly aperiodic subshift",
      "finite type",
      "large scale geometry",
      "finite collection",
      "forbidden patterns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.4572C"
    }
  }
}