Coverings of Spectral Triples
Operator Algebras
2018-04-18 v4
Abstract
It is well-known that any covering space of a Riemannian manifold has the natural structure of a Riemannian manifold. This article contains a noncommutative generalization of this fact. Since any Riemannian manifold with a Spin-structure defines a spectral triple, the spectral triple can be regarded as a noncommutative Spin-manifold. Similarly there is an algebraic construction which is a noncommutative generalization of topological covering. This article contains a construction of spectral triple on the "noncommutative covering space".
Cite
@article{arxiv.1705.08651,
title = {Coverings of Spectral Triples},
author = {Petr Ivankov},
journal= {arXiv preprint arXiv:1705.08651},
year = {2018}
}
Comments
96 pages, 25 references. arXiv admin note: substantial text overlap with arXiv:1702.07918 and text overlap with arXiv:math/0011194 by other authors