{
  "id": "1211.2347",
  "version": "v1",
  "published": "2012-11-10T20:23:11.000Z",
  "updated": "2012-11-10T20:23:11.000Z",
  "title": "Cylinders, multi-cylinders and the induced action of $Aut(F_n)$",
  "authors": [
    "Fedaa Ibrahim"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "A cylinder $C^1_u$ is the set of infinite words with fixed prefix $u$. A double-cylinder $C^2_{[1,u]}$ is \"the same\" for bi-infinite words. We show that for every word $u$ and any automorphism $\\varphi$ of the free group $F$ the image $\\varphi(C^1_u)$ is a finite union of cylinders. The analogous statement is true for double cylinders. We give (a) an algorithm, and (b) a precise formula which allows one to determine this finite union of cylinders.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-10T20:23:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "induced action",
      "multi-cylinders",
      "finite union",
      "bi-infinite words",
      "free group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2347I"
    }
  }
}