Spin structures of flat manifolds of diagonal type
Rafał Lutowski , Nansen Petrosyan , Jerzy Popko , Andrzej Szczepański
AbstractWe 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.
|Journal series||Homology Homotopy and Applications, ISSN 1532-0073, (N/A 100 pkt)|
|Publication size in sheets||0.55|
|Keywords in English||flat manifold, crystallographic group, spin structure|
|Score||= 100.0, 21-11-2019, ArticleFromJournal|
|Publication indicators||= 0; : 2018 = 0.868; : 2018 = 0.632 (2) - 2018=0.565 (5)|
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