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Asymptotically cylindrical manifolds with holonomy Spin(7). I

We construct examples of asymptotically cylindrical Riemannian 8-manifolds with holonomy group Spin(7). To our knowledge, these are the first such examples. The construction uses an extension to asymptotically cylindrical setting of Joyce's existence result for torsion-free Spin(7)-structures. One source of examples arises from `Fano-type' Kaehler 4-orbifolds with smooth anticanonical Calabi-Yau 3-fold divisors and with compatible antiholomorphic involution. We give examples using weighted projective spaces and calculate basic topological invariants of the resulting Spin(7)-manifolds.

preprint2014arXivOpen access
Alexei Kovalev
math.DG
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Alexei Kovalev

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