{
  "id": "1005.3870",
  "version": "v2",
  "published": "2010-05-21T01:14:55.000Z",
  "updated": "2010-11-30T03:53:01.000Z",
  "title": "A note on geometric constructions of bi-invariant orderings",
  "authors": [
    "Tetsuya Ito"
  ],
  "comment": "10 pages, no figures; add more explanations for the relationship to the classical construction",
  "journal": "Topology and its Applications,158 (2011) 690-696",
  "doi": "10.1016/j.topol.2011.01.015",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We construct bi-invariant total orderings of residually torsion-free nilpotent groups by using Chen's iterated integrals. This construction can be seen as a generalization of the Magnus ordering of the free groups, and equivalent to the classical construction which uses an iteration of central extensions. Our geometric construction provides a connection between bi-orderings and the rational homotopy theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-30T03:53:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F60",
      "55P62"
    ],
    "keywords": [
      "geometric construction",
      "bi-invariant orderings",
      "construct bi-invariant total orderings",
      "residually torsion-free nilpotent groups",
      "rational homotopy theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.3870I"
    }
  }
}