Fractional structures on bundle gerbe modules and fractional classifying spaces

TL;DR

This paper explores the homotopy theory of twisted Chern classes of torsion bundle gerbe modules, introducing fractional structures and classifying spaces to better understand their properties.

Contribution

It introduces the concept of fractional U-structures and extends higher structures to torsion bundle gerbe modules, providing a new universal framework.

Findings

Realization of twisted Chern classes at the classifying space level

Introduction of fractional U-structures as a universal framework

Extension of higher structures to torsion bundle gerbe modules

Abstract

We study the homotopy aspects of the twisted Chern classes of torsion bundle gerbe modules. Using Sullivan's rational homotopy theory, we realize the twisted Chern classes at the level of classifying spaces. The construction suggests a notion, which we call fractional U-structure serving as a universal framework to study the twisted Chern classes of torsion bundle gerbe modules from the perspective of classifying spaces. Based on this, we introduce and study higher fractional structures on torsion bundle gerbe modules parallel to the higher structures on ordinary vector bundles.