{
  "id": "0711.1909",
  "version": "v2",
  "published": "2007-11-13T03:29:00.000Z",
  "updated": "2007-12-19T16:51:23.000Z",
  "title": "Consistent Orientation of Moduli Spaces",
  "authors": [
    "Daniel S. Freed",
    "Michael J. Hopkins",
    "Constantin Teleman"
  ],
  "comment": "21 pages, dedicated to Nigel Hitchin on the occasion of his 60th birthday. Version 2 for publication has additional text in section 3 and makes minor corrections",
  "categories": [
    "math.AT",
    "hep-th",
    "math-ph",
    "math.KT",
    "math.MP"
  ],
  "abstract": "We give an a priori construction of the two-dimensional reduction of three-dimensional quantum Chern-Simons theory. This reduction is a two-dimensional topological quantum field theory and so determines to a Frobenius ring, which here is the twisted equivariant K-theory of a compact Lie group. We construct the theory via correspondence diagrams of moduli spaces, which we \"linearize\" using complex K-theory. A key point in the construction is to consistently orient these moduli spaces to define pushforwards; the consistent orientation induces twistings of complex K-theory. The Madsen-Tillmann spectra play a crucial role.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-12-19T16:51:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli spaces",
      "consistent orientation induces twistings",
      "two-dimensional topological quantum field theory",
      "three-dimensional quantum chern-simons theory",
      "complex k-theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 767517,
      "adsabs": "2007arXiv0711.1909F"
    }
  }
}