Flat manifolds with holonomy group Z_2^k of diagonal type

Anna Gąsior; Andrzej Szczepański

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arXiv · 1204.2127

Flat manifolds with holonomy group Z_2^k of diagonal type

Anna Gąsior·Andrzej Szczepański

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Abstract

We consider relations between two families of flat manifolds with holonomy group (Z_2)^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 ${\cal GHW}\cap {\cal RBM}$ is not empty. We also consider some class of real Bott manifolds without $\operatorname{Spin}$ and $\operatorname{Spin}^{\C}$ structure. There are given conditions for the (non)existence of such structures.

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Anna Gąsior, Andrzej Szczepański. 2012-04-10. Flat manifolds with holonomy group Z_2^k of diagonal type. https://arxiv.org/abs/1204.2127

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