Algebraic & Geometric Topology

Spin structures on almost-flat manifolds

Anna Gąsior, Nansen Petrosyan, and Andrzej Szczepański

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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.

Article information

Algebr. Geom. Topol., Volume 16, Number 2 (2016), 783-796.

Received: 5 November 2014
Revised: 6 July 2015
Accepted: 7 September 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C27: Spin and Spin$^c$ geometry
Secondary: 20H25: Other matrix groups over rings

almost-flat manifolds infra-nilmanifolds Spin structures


Gąsior, Anna; Petrosyan, Nansen; Szczepański, Andrzej. Spin structures on almost-flat manifolds. Algebr. Geom. Topol. 16 (2016), no. 2, 783--796. doi:10.2140/agt.2016.16.783.

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