A note on bundle gerbes and infinite-dimensionality

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.