Classification of spin structures on 4-dimensional almost-flat manifolds
Algebraic Topology
2018-04-12 v3 Geometric Topology
Abstract
Almost-flat manifolds were defined by Gromov as a natural generalisation of flat manifolds and as such share many of their properties. Similarly to flat manifolds, it turns out that the existence of a spin structure on an almost-flat manifold is determined by the canonical orthogonal representation of its fundamental group. Utilising this, we classify the spin structures on all four-dimensional almost-flat manifolds that are not flat. Out of 127 orientable families, there are exactly 15 that are non-spin, the rest are in fact parallelizable.
Cite
@article{arxiv.1701.03920,
title = {Classification of spin structures on 4-dimensional almost-flat manifolds},
author = {Rafał Lutowski and Nansen Petrosyan and Andrzej Szczepański},
journal= {arXiv preprint arXiv:1701.03920},
year = {2018}
}
Comments
Final version accepted for publication