Spin Structures on Flat Manifolds with Cyclic Holonomy

Abstract

We study spin structures on flat Riemannian manifolds. The main result is a necessary and sufficient condition for a flat manifold with cyclic holonomy to have a spin structure.

Key Words:

• Cyclic holonomy
• Flat manifold
• Spin structures

2000 Mathematics Subject Classification:

• 57R15
• 20H15
• 20C10

ACKNOWLEDGMENTS

We gratefully acknowledge the financial support received by the second author through the DFG Research Training Group (Graduiertenkolleg) GRK 775 “Hierarchie und Symmetrie in mathematischen Modellen” and the polish grant BW 5100-5-0039-6.

We also thank Karl-Hermann Neeb for his clarifying remarks on the meta-linear groups, and Klaus Lux for pointing out the reference to the Gagola and Garrison article.

Although it is not explicitly visible in the final version of our article, the possibility of quickly performing numerous experiments with GAP (2004) was of great help for us.

Notes

Communicated by S. K. Sehgal.