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Spin structures on almost-flat manifolds

Anna Gąsior, Nansen Petrosyan and Andrzej Szczepański

Algebraic & Geometric Topology 16 (2016) 783–796
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–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