{
  "id": "math/0511478",
  "version": "v2",
  "published": "2005-11-19T01:47:05.000Z",
  "updated": "2006-09-12T15:04:41.000Z",
  "title": "Clusters, currents and Whitehead's algorithm",
  "authors": [
    "Ilya Kapovich"
  ],
  "comment": "Updated version, to appear in \"Experimental Mathematics\"",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Using geodesic currents, we provide a theoretical justification for some of the experimental results regarding the behavior of Whitehead's algorithm on non-minimal inputs, that were obtained by Haralick, Miasnikov and Myasnikov via pattern recognition methods. In particular we prove that the images of \"random\" elements of a free group $F$ under the automorphisms of $F$ form \"clusters\" that share similar normalized Whitehead graphs and similar behavior with respect to Whitehead's algorithm.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-09-12T15:04:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "whiteheads algorithm",
      "share similar normalized whitehead graphs",
      "non-minimal inputs",
      "pattern recognition methods",
      "free group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11478K"
    }
  }
}