Noncommutative spectral geometry of Riemannian foliations

TL;DR

This paper develops a noncommutative geometric framework for Riemannian foliations by constructing spectral triples and analyzing their spectral properties.

Contribution

It introduces a novel method to associate spectral triples with Riemannian foliations and describes their dimension spectrum.

Findings

Spectral triples are constructed for Riemannian foliations.

The dimension spectrum of these spectral triples is characterized.

This work bridges noncommutative geometry and foliation theory.

Abstract

We construct spectral triples in a sense of noncommutative differential geometry, associated with a Riemannian foliation on a compact manifold, and describe its dimension spectrum.