{
  "id": "1310.2254",
  "version": "v3",
  "published": "2013-10-08T20:02:31.000Z",
  "updated": "2014-05-12T19:42:54.000Z",
  "title": "Stable Commutator Length in Amalgamated Free Products",
  "authors": [
    "Timothy Susse"
  ],
  "comment": "28 pages, 5 figures. Corrected typographical errors, changed exposition, added new results on quasirationality",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We show that stable commutator length is rational on free products of free Abelian groups amalgamated over $\\mathbb{Z}^k$, a class of groups containing the fundamental groups of all torus knot complements. We consider a geometric model for these groups and parameterize all surfaces with specified boundary mapping to this space. Using this work we provide a topological algorithm to compute stable commutator length in these groups. Further, we use the methods developed to show that in free products of cyclic groups the stable commutator length of a fixed varies quasirationally in the orders of the free factors.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-12T19:42:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M07",
      "20F65",
      "20J05",
      "20F12",
      "57M25"
    ],
    "keywords": [
      "stable commutator length",
      "amalgamated free products",
      "torus knot complements",
      "fundamental groups",
      "free abelian groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.2254S"
    }
  }
}