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arXiv · 1701.03920

Classification of spin structures on 4-dimensional almost-flat manifolds

Rafał Lutowski·Nansen Petrosyan·Andrzej Szczepański
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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.

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Rafał Lutowski, Nansen Petrosyan, Andrzej Szczepański. 2017-01-14. Classification of spin structures on 4-dimensional almost-flat manifolds. https://doi.org/10.1112/s0025579317000560

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