{
  "id": "2007.06239",
  "version": "v1",
  "published": "2020-07-13T08:47:57.000Z",
  "updated": "2020-07-13T08:47:57.000Z",
  "title": "A lattice version of the Atiyah-Singer index theorem",
  "authors": [
    "Mayuko Yamashita"
  ],
  "comment": "23 pages",
  "categories": [
    "math.DG",
    "math-ph",
    "math.KT",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We formulate and prove a lattice version of the Atiyah-Singer index theorem. The main theorem gives a $K$-theoretic formula for an index-type invariant of operators on lattice approximations of closed integral affine manifolds. We apply the main theorem to an index problem in lattice gauge theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-13T08:47:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "atiyah-singer index theorem",
      "lattice version",
      "main theorem",
      "closed integral affine manifolds",
      "lattice gauge theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}