A note on bundle gerbes and infinite-dimensionality

TL;DR

This paper proves that for certain bundle gerbes over simply-connected base spaces with connected finite-dimensional fibers, the Dixmier-Douady class must be torsion, correcting previous results in the literature.

Contribution

It establishes a new torsion property of the Dixmier-Douady class for a class of bundle gerbes, extending and correcting earlier findings.

Findings

Dixmier-Douady class is torsion under specified conditions

Correction of earlier results on bundle gerbes

Extension to broader class of fiber bundles

Abstract

Let $(P, Y)$ be a bundle gerbe over a fibre bundle $Y \to M$. We show that if $M$ is simply-connected and the fibres of $Y \to M$ are connected and finite-dimensional then the Dixmier-Douady class of $(P, Y)$ is torsion. This corrects and extends an earlier result of the first author.