Geodesic
Multiple vector bundles: cores, splittings and decompositions
Theory and applications of categories, Tome 35 (2020), pp. 665-699

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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.

Publié le :
Classification : 53C05 (Primary), 18F15, 55R65 (Secondary)
Keywords: n-fold vector bundle atlas, linear decomposition 
@article{TAC_2020_35_a18,
     author = {Malte Heuer and Madeleine Jotz Lean},
     title = {Multiple vector bundles: cores, splittings and decompositions},
     journal = {Theory and applications of categories},
     pages = {665--699},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a18/}
}
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Malte Heuer; Madeleine Jotz Lean. Multiple vector bundles: cores, splittings and decompositions. Theory and applications of categories, Tome 35 (2020), pp. 665-699. http://geodesic.mathdoc.fr/item/TAC_2020_35_a18/