{
  "id": "2010.05890",
  "version": "v1",
  "published": "2020-10-12T17:39:42.000Z",
  "updated": "2020-10-12T17:39:42.000Z",
  "title": "$U_q(sl(2))-$quantum invariants unified via intersections of embedded Lagrangians",
  "authors": [
    "Cristina Ana-Maria Anghel"
  ],
  "comment": "18 pages, comments welcome",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "In this paper we prove a unified model for $U_q(sl(2))$ quantum invariants through intersections of embedded Lagrangians in configuration spaces. More specifically, we construct a state sum of Lagrangian intersections in the configuration space in the punctured disc, which leads to a polynomial in three variables. This polynomial recovers the coloured Jones polynomial and the coloured Alexander polynomial through certain specialisation of coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-12T17:39:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "20F36",
      "16T05",
      "16T25"
    ],
    "keywords": [
      "quantum invariants",
      "embedded lagrangians",
      "configuration space",
      "state sum",
      "lagrangian intersections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}