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, (A 25 pkt)|
|Publication size in sheets||0.55|
|Keywords in English||flat manifold, crystallographic group, spin structure|
|Score||= 25.0, 24-07-2019, ArticleFromJournal|
|Publication indicators||: 2016 = 0.474; : 2017 = 0.711 (2) - 2017=0.713 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.