Principal Bundles and the Dixmier Douady Class

TL;DR

This paper systematically explores the reduction and extension of principal bundle structure groups, applying these techniques to study the Dixmier-Douady class in contexts like string structures and quantum field theory.

Contribution

It introduces new methods for analyzing the Dixmier-Douady class through principal bundle modifications, connecting topology with quantum field theory applications.

Findings

Techniques for reducing and extending principal bundle groups

Applications to Dixmier-Douady class in string structures

Connections to quantum field theory contexts

Abstract

A systematic consideration of the problem of the reduction and extension of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the Dixmier-Douady class in various contexts including string structures, U-res bundles and other examples motivated by considerations from quantum field theory.