{
  "id": "2007.09828",
  "version": "v1",
  "published": "2020-07-20T01:40:25.000Z",
  "updated": "2020-07-20T01:40:25.000Z",
  "title": "Over then Under Tangles",
  "authors": [
    "Dror Bar-Natan",
    "Zsuzsanna Dancso",
    "Roland van der Veen"
  ],
  "comment": "34 pages, lots of figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Brilliant wrong ideas should not be buried and forgotten. Instead, they should be mined for the gold that lies underneath the layer of wrong. In this paper we explain how \"over then under tangles\" lead to an easy classification of knots, and under the surface, also to some valid mathematics: a separation theorem for braids and virtual braids. We end the paper with an overview of other instances where \"over then under\" ideas play a role: a topological understanding of the Drinfel'd double construction of quantum group theory, the quantization of Lie bialgebras, and more.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-20T01:40:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "brilliant wrong ideas",
      "quantum group theory",
      "lie bialgebras",
      "lies underneath",
      "drinfeld double construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}