{
  "id": "2104.02049",
  "version": "v1",
  "published": "2021-04-05T17:57:00.000Z",
  "updated": "2021-04-05T17:57:00.000Z",
  "title": "Witten-Reshetikhin-Turaev invariants for 3-manifolds from Lagrangian intersections in configuration spaces",
  "authors": [
    "Cristina Ana-Maria Anghel"
  ],
  "comment": "21 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we construct a topological model for the Witten-Reshetikhin-Turaev invariants for $3$-manifolds as graded intersection pairings of homology classes in configuration spaces. More precisely, for a fixed level $\\cN \\in \\N$ we show that the level $\\cN$ WRT invariant for a $3-$manifold is a state sum of Lagrangian intersections in a covering of a fixed configuration space in the punctured disk. This model brings a new perspective on the structure of the level $\\cN$ Witten-Reshetikhin-Turaev invariant, showing that it is completely encoded by the intersection points between certain Lagrangian submanifolds in a fixed configuration space, with additional gradings which come from a particular choice of a local system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-05T17:57:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "witten-reshetikhin-turaev invariant",
      "lagrangian intersections",
      "fixed configuration space",
      "local system",
      "model brings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}