{
  "id": "2108.10246",
  "version": "v1",
  "published": "2021-08-23T15:38:03.000Z",
  "updated": "2021-08-23T15:38:03.000Z",
  "title": "Framed Knotoids and Their Quantum Invariants",
  "authors": [
    "Wout Moltmaker"
  ],
  "comment": "26 pages, 34 figures, comments are welcome",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "We modify the definition of spherical knotoids to include a framing, in analogy to framed knots, and define a further modification that includes a secondary 'coframing' to obtain 'biframed' knotoids. We exhibit topological spaces whose ambient isotopy classes are in one-to-one correspondence with framed and biframed knotoids respectively. We then show how framed and biframed knotoids allow us to generalize quantum knot invariants to a knotoid setting, leading to the construction of general Reshetikhin-Turaev type biframed knotoid invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-23T15:38:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K12",
      "57K16"
    ],
    "keywords": [
      "quantum invariants",
      "framed knotoids",
      "general reshetikhin-turaev type biframed knotoid",
      "reshetikhin-turaev type biframed knotoid invariants",
      "generalize quantum knot invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}