 Orientation of a vector bundle (source code)

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= Orientation of a vector bundle

This is a fiberwise <orientation> compatible with local trivializations of a <vector bundle>. An $R$-orientation of a rank-$d$ vector bundle is a coherent choice of generator of $H^d(E_b,E_b\setminus\{0\};R)$ for every fiber, equivalently a <Thom class> with the corresponding fiberwise restriction.

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