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.
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