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

Rafał Lutowski , Nansen Petrosyan , Andrzej Szczepański


Almost-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.
Author Rafał Lutowski (FMPI / IM)
Rafał Lutowski,,
- Institute of Mathematics
, Nansen Petrosyan
Nansen Petrosyan,,
, Andrzej Szczepański (FMPI / IM)
Andrzej Szczepański,,
- Institute of Mathematics
Journal seriesMathematika, ISSN 0025-5793, (A 25 pkt)
Issue year2018
Publication size in sheets0.65
Keywords in Englishalmost-flat manifolds, spin structures
ASJC Classification2600 General Mathematics
Languageen angielski
Score (nominal)25
Score sourcejournalList
ScoreMinisterial score = 25.0, 28-01-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 0.983; WoS Impact Factor: 2018 = 0.689 (2) - 2018=0.724 (5)
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