{
  "id": "math/0409087",
  "version": "v1",
  "published": "2004-09-06T17:43:13.000Z",
  "updated": "2004-09-06T17:43:13.000Z",
  "title": "Commutators and squares in free groups",
  "authors": [
    "Sucharit Sarkar"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-27.abs.html",
  "journal": "Algebr. Geom. Topol. 4 (2004) 595-602",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let F_2 be the free group generated by x and y. In this article, we prove that the commutator of x^m and y^n is a product of two squares if and only if mn is even. We also show using topological methods that there are infinitely many obstructions for an element in F_2 to be a product of two squares.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-06T17:43:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F12",
      "57M07"
    ],
    "keywords": [
      "commutator",
      "free group",
      "topological methods"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}