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Cohomology classes associated to vector bundles. Includes Stiefel-Whitney classes, Chern classes, Pontryagin classes, and the Euler class.
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Splitting principle for real vector bundles
I'm reading the Book of John Roe, Elliptic Operators, Topology and Asymptotic Methods and got stuck at Lemma 2.27.
i) How does this lemma show that a real vector bundle can be given by a pullback of …