Coverings of Spectral Triples
Petr Ivankov

TL;DR
This paper generalizes the classical concept of covering spaces of Riemannian manifolds to the noncommutative setting using spectral triples, providing a framework for noncommutative coverings.
Contribution
It introduces a construction of spectral triples on noncommutative covering spaces, extending classical geometric ideas to noncommutative geometry.
Findings
Established a noncommutative analogue of covering space theory
Constructed spectral triples for noncommutative coverings
Bridged classical and noncommutative geometric concepts
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".
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Algebra and Geometry · Advanced Topics in Algebra
