{
  "id": "1904.09045",
  "version": "v1",
  "published": "2019-04-19T00:47:15.000Z",
  "updated": "2019-04-19T00:47:15.000Z",
  "title": "Dense orderings in the space of left-orderings of a group",
  "authors": [
    "Adam Clay",
    "Tessa Reimer"
  ],
  "comment": "12 pages, 2 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "Every left-invariant ordering of a group is either discrete, meaning there is a least element greater than the identity, or dense. Corresponding to this dichotomy, the spaces of left, Conradian, and bi-orderings of a group are naturally partitioned into two subsets. This note investigates the structure of this partition, specifically the set of dense orderings of a group and its closure within the space of orderings. We show that for bi-orderable groups this closure will always contain the space of Conradian orderings---and often much more. In particular, the closure of the set of dense orderings of the free group is the entire space of left-orderings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-19T00:47:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06F15",
      "20F60"
    ],
    "keywords": [
      "dense orderings",
      "left-orderings",
      "conradian orderings-and",
      "free group",
      "element greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}