Constructing Compact 8-Manifolds with Holonomy Spin(7) from Calabi—Yau Orbifolds

  • Dominic Joyce
Part of the Progress in Mathematics book series (PM, volume 202)


Compact Riemannian 7- and 8-manifolds with holonomy G2 and Spin(7) were first constructed by the author in 1994-5, by resolving orb­ifolds T7/F and T8/F. This paper describes a new construction of compact 8-manifolds with holonomy Spin(7). We start with a Calabi—Yau 4-orbifold Y with isolated singularities of a special kind. We divide by an antiholomorphic involution a of Y to get a real 8-orbifold Z = Y/(a). Then we resolve the singularities of Z to get a compact 8-manifold M, which has metrics with ho­lonomy Spin(7). Manifolds constructed in this way typically have large fourth Betti number b4(M).


Betti Number Holonomy Group Injectivity Radius Weighted Projective Space Crepant Resolution 
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© Springer Basel AG 2001

Authors and Affiliations

  • Dominic Joyce
    • 1
  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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