Abstract
A vector bundle is a bundle with an additional vector space structure on each fibre. The concept arose from the study of tangent vector fields to smooth geometric objects, e.g., spheres, projective spaces, and, more generally, manifolds. The vector bundle structure is so rich that the set of isomorphism classes of k-dimensional vector bundles over a paracompact space B is in a natural bijective correspondence with the set of homotopy classes of mappings of B into the Grassmann manifold of k-dimensional subspaces in infinite-dimensional space.
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© 1994 Springer Science+Business Media New York
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Husemoller, D. (1994). Vector Bundles. In: Fibre Bundles. Graduate Texts in Mathematics, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2261-1_3
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DOI: https://doi.org/10.1007/978-1-4757-2261-1_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2263-5
Online ISBN: 978-1-4757-2261-1
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