Abstract
In the first section, we show that, up to isomorphism, vector bundles are just locally trivial fibre bundles with a finite-dimensional vector space V as fibre and GL(V), the group of automorphisms of V, as a structure group. This is done by examining how trivial bundles are pieced together, using systems of transition functions to define a general locally trivial fibre bundle. We can apply this analysis to prove a theorem which says that any continuous functorial operation on vector spaces determines an operation on vector bundles. This allows construction of tensor products, exterior products, etc., of vector bundles.
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© 1994 Springer Science+Business Media New York
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Husemoller, D. (1994). Local Coordinate Description of Fibre Bundles. In: Fibre Bundles. Graduate Texts in Mathematics, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2261-1_5
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DOI: https://doi.org/10.1007/978-1-4757-2261-1_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2263-5
Online ISBN: 978-1-4757-2261-1
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