A note on $n$-gerbes and transgressions

Abstract

In this note we provide an explicit interpretation of a class of $(q-1)$-gerbes with multi-layered connections in terms of transgression of a fibrewise closed $q$-form on a fibration to a closed $(q+1)$-form on the base manifold, with the basic example of the Euler class of an oriented vector bundle in mind ($q\ge 0$). Picken's and Ferreira–Gothen’s $n$-gerbopoles are discussed from this point of view. Furthermore, string structures (à la Cocquereaux–Pilch and à la Spera–Wurzbacher) are briefly addressed and recast within the proposed framework.