Kirill C.H. Mackenzie (University of Sheffield)
K.Mackenzie@sheffield.ac.uk
A double vector bundle (= a vector bundle object in the category of vector bundles) has two duals, both themselves double vector bundles, and these duals are themselves in duality. Thus double vector bundles have a kind of `three--step duality' which is an entirely new phenomenon. We show in this talk that this duality can be naturally understood in terms of triple structures. By considering in turn the duality for triple vector bundles, we show how the general multiple case develops.