Algebraic Versus Spectral Torsion

TL;DR

This paper explores the relationship between spectral torsion and algebraic torsion within noncommutative geometry, focusing on the example of a product space involving a Riemannian manifold and a two-point space.

Contribution

It establishes a connection between spectral and algebraic torsion in the context of noncommutative differential calculi on specific geometric examples.

Findings

Spectral torsion is related to algebraic torsion in the studied example.

The analysis provides insights into the structure of noncommutative geometries.

Results may inform future research on torsion in noncommutative spaces.

Abstract

We relate the recently defined spectral torsion with the algebraic torsion of noncommutative differential calculi on the example of the almost-commutative geometry of the product of a closed oriented Riemannian spin manifold $M$ with the two-point space $\mathcal Z_2$.