{
  "id": "0705.2623",
  "version": "v1",
  "published": "2007-05-18T19:42:18.000Z",
  "updated": "2007-05-18T19:42:18.000Z",
  "title": "Densely ordered braid subgroups",
  "authors": [
    "Adam Clay",
    "Dale Rolfsen"
  ],
  "categories": [
    "math.GR",
    "math.AT"
  ],
  "abstract": "Dehornoy showed that the Artin braid groups $B_n$ are left-orderable. This ordering is discrete, but we show that, for $n >2$ the Dehornoy ordering, when restricted to certain natural subgroups, becomes a dense ordering. Among subgroups which arise are the commutator subgroup and the kernel of the Burau representation (for those $n$ for which the kernel is nontrivial). These results follow from a characterization of least positive elements of any normal subgroup of $B_n$ which is discretely ordered by the Dehornoy ordering.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-18T19:42:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F60"
    ],
    "keywords": [
      "densely ordered braid subgroups",
      "artin braid groups",
      "normal subgroup",
      "burau representation",
      "dehornoy ordering"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.2623C"
    }
  }
}