Constructing Compact 8-Manifolds with Holonomy Spin(7) from Calabi—Yau Orbifolds
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).
KeywordsBetti Number Holonomy Group Injectivity Radius Weighted Projective Space Crepant Resolution
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