Unoriented Spectral Triples
arXiv:1712.03752
Abstract
Any oriented Riemannian manifold with a Spin-structure defines a spectral triple, so the spectral triple can be regarded as a noncommutative Spin-manifold. Otherwise for any unoriented Riemannian manifold there is the two-fold covering by oriented Riemannian manifold. Moreover there are noncommutative generalizations of finite-fold coverings. This circumstances yield a notion of unoriented spectral triple which is covered by oriented one.
11 pages, 11 references. arXiv admin note: text overlap with arXiv:1705.08651, arXiv:1702.07918