Spin structures of flat manifolds of diagonal type

Rafał Lutowski , Nansen Petrosyan , Jerzy Popko , Andrzej Szczepański

Abstract

We give a novel and purely combinatorial description of Stiefel–Whitney classes of closed flat manifolds with diagonal holonomy representation. Using this description, for each integer d at least two, we construct non-spin closed oriented flat manifolds with holonomy group Zd2 with the property that all of their finite proper covers have a spin structure. Moreover, all such covers have trivial Stiefel–Whitney classes. In contrast to the case of real Bott manifolds, this shows that for a general closed flat manifold the existence of a spin structure may not be detected by its finite proper covers.
Author Rafał Lutowski (FMPI / IM)
Rafał Lutowski,,
- Institute of Mathematics
, Nansen Petrosyan
Nansen Petrosyan,,
-
, Jerzy Popko (FMPI / IM)
Jerzy Popko,,
- Institute of Mathematics
, Andrzej Szczepański (FMPI / IM)
Andrzej Szczepański,,
- Institute of Mathematics
Journal seriesHomology Homotopy and Applications, ISSN 1532-0073, (N/A 100 pkt)
Issue year2019
Vol21
No2
Pages333-344
Publication size in sheets0.55
Keywords in Englishflat manifold, crystallographic group, spin structure
ASJC Classification2601 Mathematics (miscellaneous)
DOIDOI:10.4310/HHA.2019.v21.n2.a18
URL https://www.intlpress.com/site/pub/pages/journals/items/hha/content/vols/0021/0002/a018/
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 21-11-2019, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.868; WoS Impact Factor: 2018 = 0.632 (2) - 2018=0.565 (5)
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