Noncommutative principal torus bundles via parametrised strict deformation quantization

TL;DR

This paper develops a parametrised strict deformation quantization framework to classify noncommutative principal torus bundles, extending the theory to non-principal cases and providing new insights into their structure.

Contribution

It introduces a parametrised approach to strict deformation quantization and applies it to classify noncommutative principal torus bundles, including a proposed definition for non-principal cases.

Findings

Classification of noncommutative principal torus bundles achieved

Extension of deformation quantization to parametrised setting

Proposal of a definition for non-principal torus bundles

Abstract

In this paper, we initiate the study of a parametrised version of Rieffel's strict deformation quantization. We apply it to give a classification of noncommutative principal torus bundles, in terms of parametrised strict deformation quantization of ordinary principal torus bundles. The paper also contains a putative definition of noncommutative non-principal torus bundles.