The geometry of determinant line bundles in noncommutative geometry

TL;DR

This paper explores the geometric structure of determinant line bundles linked to families of spectral triples in noncommutative geometry, providing examples to illustrate the theoretical findings.

Contribution

It introduces a detailed study of the geometry of determinant line bundles in the context of noncommutative spectral triples and their moduli spaces.

Findings

Characterization of determinant line bundle geometry in noncommutative setting

Examples illustrating the theoretical framework in noncommutative geometry

Insights into the structure of moduli spaces of connections

Abstract

This paper is concerned with the study of the geometry of determinant line bundles associated to families of spectral triples parametrized by the moduli space of gauge equivalent classes of Hermitian connections on a Hermitian finite projective module. We illustrate our results with some examples that arise in noncommutative geometry.