Unoriented Spectral Triples
Operator Algebras
2017-12-12 v1
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.
Cite
@article{arxiv.1712.03752,
title = {Unoriented Spectral Triples},
author = {Petr Ivankov},
journal= {arXiv preprint arXiv:1712.03752},
year = {2017}
}
Comments
11 pages, 11 references. arXiv admin note: text overlap with arXiv:1705.08651, arXiv:1702.07918