{
  "id": "1803.06382",
  "version": "v1",
  "published": "2018-03-16T19:44:59.000Z",
  "updated": "2018-03-16T19:44:59.000Z",
  "title": "Harmonic spinors on the Davis hyperbolic 4-manifold",
  "authors": [
    "John G. Ratcliffe",
    "Daniel Ruberman",
    "Steven T. Tschantz"
  ],
  "comment": "33 pages and 2 figures",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "In this paper we use the G-spin theorem to show that the Davis hyperbolic 4-manifold admits harmonic spinors. This is the first example of a closed hyperbolic 4-manifold that admits harmonic spinors. We also explicitly describe the Spinor bundle of a spin hyperbolic 2- or 4-manifold and show how to calculated the subtle sign terms in the G-spin theorem for an isometry, with isolated fixed points, of a closed spin hyperbolic 2- or 4-manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-16T19:44:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C27"
    ],
    "keywords": [
      "davis hyperbolic",
      "admits harmonic spinors",
      "g-spin theorem",
      "subtle sign terms",
      "first example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}