Real Spectral Triples over Noncommutative Bieberbach Manifolds
arXiv:1301.2240 · doi:10.1016/j.geomphys.2013.05.003
Abstract
We classify and construct all real spectral triples over noncommutative Bieberbach manifolds, which are restrictions of irreducible real equivariant spectral triple over the noncommutative three-torus. We show that in the classical case the constructed geometries correspond exactly to spin structures over Bieberbach manifolds and the Dirac operators constructed for a flat metric.
18 pages