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In this note we provide an explicit interpretation of a class of -gerbes with multi-layered connections in terms of transgression of a fibrewise closed -form on a fibration to a closed -form on the base manifold, with the basic example of the Euler class of an oriented vector bundle in mind (). Picken's and Ferreira–Gothen’s -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.
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Mauro Spera, A note on <var>n</var>-gerbes and transgressions. Port. Math. 68 (2011), no. 4, pp. 381–387