{
  "id": "math/0109166",
  "version": "v1",
  "published": "2001-09-22T22:12:46.000Z",
  "updated": "2001-09-22T22:12:46.000Z",
  "title": "Free actions on handlebodies",
  "authors": [
    "Darryl McCullough",
    "Marcus Wanderley"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "The equivalence (or weak equivalence) classes of orientation-preserving free actions of a finite group G on an orientable 3-dimensional handlebody of genus g can be enumerated in terms of sets of generators of G. They correspond to the equivalence classes of generating n-vectors of elements of G, where n=1+(g-1)/|G|, under Nielsen equivalence (or weak Nielsen equivalence). For abelian and dihedral G, this allows a complete determination of the equivalence and weak equivalence classes of actions for all genera. Additional information is obtained for solvable groups and for the groups PSL(2,3^p) with p prime. For all G, there is only one equivalence class of actions on the genus g handlebody if g is at least 1+r(G)|G|, where r(G) is the maximal length of a chain of subgroups of G. There is a stabilization process that sends an equivalence class of actions to an equivalence class of actions on a higher genus, and some results about its effects are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-09-22T22:12:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M60"
    ],
    "keywords": [
      "handlebody",
      "weak nielsen equivalence",
      "weak equivalence classes",
      "orientation-preserving free actions",
      "complete determination"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......9166M"
    }
  }
}