Classification of spin structures on 4-dimensional almost-flat manifolds
Rafał Lutowski , Nansen Petrosyan , Andrzej Szczepański
AbstractAlmost-flat manifolds were defined by Gromov as a natural generalization 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. Utilizing this, we classify the spin structures on all four-dimensional almost-flat manifolds that are not flat. Out of 127 orientable families, we show that there are exactly 15 that are non-spin, the rest are, in fact, parallelizable.
|Journal series||Mathematika, ISSN 0025-5793, (A 25 pkt)|
|Publication size in sheets||0.65|
|Keywords in English||almost-flat manifolds, spin structures|
|Score||= 25.0, 28-01-2020, ArticleFromJournal|
|Publication indicators||= 0; : 2017 = 0.983; : 2018 = 0.689 (2) - 2018=0.724 (5)|
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