Spin structures on almost-flat manifolds

Gąsior, Anna; Petrosyan, Nansen; Szczepański, Andrzej

doi:10.2140/agt.2016.16.783

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Spin structures on almost-flat manifolds

Anna Gąsior, Nansen Petrosyan and Andrzej Szczepański

Algebraic & Geometric Topology 16 (2016) 783–796

DOI: 10.2140/agt.2016.16.783

Abstract

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 $4$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn></math>$ –dimensional orientable almost-flat manifolds with cyclic holonomy that do not admit a Spin structure.

Keywords

almost-flat manifolds, infra-nilmanifolds, Spin structures

Mathematical Subject Classification 2010

Primary: 53C27

Secondary: 20H25

References

Publication

Received: 5 November 2014

Revised: 6 July 2015

Accepted: 7 September 2015

Published: 26 April 2016

Authors

Anna Gąsior
Maria Curie-Skłodowska University 20-031 Lublin Poland

Nansen Petrosyan
Department of Mathematics University of Southampton Southampton SO17 1BJ UK

Andrzej Szczepański
Institute of Mathematics University of Gdańsk 80-952 Gdańsk Poland

Volume 16, issue 2 (2016)