Geodesic
Spin structures on almost-flat manifolds
Gąsior, Anna1 ; Petrosyan, Nansen2 ; Szczepański, Andrzej3
1Maria Curie-Skłodowska University, 20-031 Lublin, Poland
2Department of Mathematics, University of Southampton, Southampton SO17 1BJ, UK
3Institute of Mathematics, University of Gdańsk, 80-952 Gdańsk, Poland
Algebraic and Geometric Topology, Tome 16 (2016) no. 2, pp. 783-796
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We give a necessary and sufficient condition for almost-flat manifolds with cyclic holonomy to admit a Spin structure. Using this condition we find all 4–dimensional orientable almost-flat manifolds with cyclic holonomy that do not admit a Spin structure.

DOI : 10.2140/agt.2016.16.783
Classification : 53C27, 20H25
Keywords: almost-flat manifolds, infra-nilmanifolds, Spin structures

Gąsior, Anna  1   ; Petrosyan, Nansen  2   ; Szczepański, Andrzej  3

1 Maria Curie-Skłodowska University, 20-031 Lublin, Poland
2 Department of Mathematics, University of Southampton, Southampton SO17 1BJ, UK
3 Institute of Mathematics, University of Gdańsk, 80-952 Gdańsk, Poland 
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Gąsior, Anna; Petrosyan, Nansen; Szczepański, Andrzej. Spin structures on almost-flat manifolds. Algebraic and Geometric Topology, Tome 16 (2016) no. 2, pp. 783-796. doi: 10.2140/agt.2016.16.783

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