{
  "id": "1608.08295",
  "version": "v1",
  "published": "2016-08-30T01:27:41.000Z",
  "updated": "2016-08-30T01:27:41.000Z",
  "title": "Generalized torsion elements and bi-orderability of $3$--manifold groups",
  "authors": [
    "Kimihiko Motegi",
    "Masakazu Teragaito"
  ],
  "comment": "11 pages, no figure",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "It is well known that a bi-orderable group has no generalized torsion element, but the converse does not hold in general. We conjecture that the converse holds for the fundamental groups of $3$--manifolds, and verify the conjecture for non-hyperbolic, geometric $3$--manifolds. We also confirm the conjecture for an infinite family of closed hyperbolic $3$--manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-30T01:27:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M05",
      "06F15"
    ],
    "keywords": [
      "generalized torsion element",
      "manifold groups",
      "bi-orderability",
      "conjecture",
      "converse holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}