Multiple vector bundles: cores, splittings and decompositions

Malte Heuer and Madeleine Jotz Lean

This paper introduces ∞- and n-fold vector bundles as special functors from the ∞- and n-cube categories to the category of smooth manifolds. We study the cores and "n-pullbacks" of n-fold vector bundles and we prove that any n-fold vector bundle admits a non-canonical isomorphism to a decomposed n-fold vector bundle. A colimit argument then shows that ∞-fold vector bundles admit as well non-canonical decompositions. For the convenience of the reader, the case of triple vector bundles is discussed in detail.

Keywords: n-fold vector bundle atlas, linear decomposition

2020 MSC: 53C05 (Primary), 18F15, 55R65 (Secondary)

Theory and Applications of Categories, Vol. 35, 2020, No. 19, pp 665-699.

Published 2020-05-26.

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