English

Asymptotically cylindrical manifolds with holonomy Spin(7). I

Differential Geometry 2014-12-31 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1309.5027,
  title  = {Asymptotically cylindrical manifolds with holonomy Spin(7). I},
  author = {Alexei Kovalev},
  journal= {arXiv preprint arXiv:1309.5027},
  year   = {2014}
}

Comments

28 pages; v2 some typos and inaccuracies corrected

R2 v1 2026-06-22T01:30:25.195Z