{
  "id": "math/9910002",
  "version": "v1",
  "published": "1999-10-01T11:07:45.000Z",
  "updated": "1999-10-01T11:07:45.000Z",
  "title": "A new construction of compact 8-manifolds with holonomy Spin(7)",
  "authors": [
    "Dominic Joyce"
  ],
  "comment": "43 pages, LaTeX, uses packages amstex and amssymb",
  "journal": "J.Diff.Geom. 53 (1999) 89-130",
  "categories": [
    "math.DG",
    "hep-th"
  ],
  "abstract": "The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. In a previous paper (Invent. math. 123 (1996), 507-552) the author constructed the first examples of compact 8-manifolds with holonomy Spin(7), by resolving orbifolds T^8/G, where T^8 is the 8-torus and G a finite group of automorphisms of T^8. This paper describes a different construction of compact 8-manifolds with holonomy Spin(7). We start with a Calabi-Yau 4-orbifold Y with isolated singularities, and an isometric, antiholomorphic involution \\sigma of Y fixing only the singular points. Let Z=Y/<\\sigma>. Then Z is an orbifold with isolated singularities, and a natural Spin(7)-structure. We resolve the singular points of Z to get a compact 8-manifold M, and show that M has holonomy Spin(7). Taking Y to be a hypersurface in a complex weighted projective space, we construct new examples of compact 8-manifolds with holonomy Spin(7), and calculate their Betti numbers b^k. The fourth Betti number b^4 tends to be rather large, as high as 11,662 in one example.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-10-01T11:07:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "holonomy spin",
      "construction",
      "singular points",
      "exceptional holonomy groups",
      "fourth betti number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 508123,
      "adsabs": "1999math.....10002J"
    }
  }
}