{
  "id": "2106.10736",
  "version": "v1",
  "published": "2021-06-20T18:10:58.000Z",
  "updated": "2021-06-20T18:10:58.000Z",
  "title": "Circular orderability of 3-manifold groups",
  "authors": [
    "Idrissa Ba",
    "Adam Clay"
  ],
  "comment": "33 pages, 2 figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "This paper initiates the study of circular orderability of $3$-manifold groups, motivated by the L-space conjecture. We show that a compact, connected, $\\mathbb{P}^2$-irreducible $3$-manifold has a circularly orderable fundamental group if and only if there exists a finite cyclic cover with left-orderable fundamental group, which naturally leads to a \"circular orderability version\" of the L-space conjecture. We also show that the fundamental groups of almost all graph manifolds are circularly orderable, and contrast the behaviour of circularly orderability and left-orderability with respect to the operations of Dehn surgery and taking cyclic branched covers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-20T18:10:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M60",
      "57M50",
      "03C15",
      "06F15",
      "20F60"
    ],
    "keywords": [
      "l-space conjecture",
      "circular orderability version",
      "finite cyclic cover",
      "cyclic branched covers",
      "paper initiates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}