Abstract
In this chapter we consider fibre bundles with the classical groups as fibre. By studying these bundles, we are able to calculate homotopy groups of the Stiefel varieties and classical groups. In the course of the development, we derive a homotopy classification for general fibre bundles over a suspension. Using this classification theorem and the homotopy groups of the classical groups, we are able to classify all vector bundles over a sphere of dimension ≦4.
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© 1994 Springer Science+Business Media New York
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Husemoller, D. (1994). Calculations Involving the Classical Groups. In: Fibre Bundles. Graduate Texts in Mathematics, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2261-1_8
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DOI: https://doi.org/10.1007/978-1-4757-2261-1_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2263-5
Online ISBN: 978-1-4757-2261-1
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