Spin structures of flat manifolds of diagonal type

Abstract

For each integer $d$ at least two, we construct non-spin closed oriented flat manifolds with holonomy group ${\mathbb{Z}}_2^d$ and with the property that all of their finite proper covers have a spin structure. Moreover, all such covers have trivial Stiefel-Whitney classes.

13 pages

References in corpus (1)

• Spin-structures on real Bott manifolds

Cited by in corpus (2)

• Spin${}^c$ structures on Hantzsche-Wendt manifolds
• Spin-structures on real Bott manifolds with Kähler structures