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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)

Abstract

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).

Keywords

Betti Number Holonomy Group Injectivity Radius Weighted Projective Space Crepant Resolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

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

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