Flat manifolds with holonomy group Z₂^k of diagonal type

2012/04/10 by Gąsior, Anna, Szczepański, Andrzej
#20H15 #53C24 #53C27 #53C29 #57S25 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1204.2127

Abstract

We consider relations between two families of flat manifolds with holonomy group (Z₂)^k of diagonal type. The family \cal RBM of real Bott manifolds and the family \cal GHW of generalized Hantzsche-Wendt manifolds. In particular, we prove that the intersection \cal GHW∩ \cal RBM is not empty. We also consider some class of real Bott manifolds without Spin and Spin^\C structure. There are given conditions for the (non)existence of such structures.

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