Real Spectral Triples over Noncommutative Bieberbach Manifolds
classification
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bieberbachmanifoldsnoncommutativerealspectralconstructedtriplescase
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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.
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