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

Rafał Lutowski , Nansen Petrosyan , Andrzej Szczepański

Abstract

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
Vol64
No1
Pages253-266
Publication size in sheets0.65
Keywords in Englishalmost-flat manifolds, spin structures
DOIDOI:10.1112/S0025579317000560
Languageen angielski
Score (nominal)25
ScoreMinisterial score = 25.0, 06-04-2018, ArticleFromJournal
Ministerial score (2013-2016) = 25.0, 06-04-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 0.667 (2) - 2016=0.896 (5)
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