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7:40 PM
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Q: Lawson and Michelsohn's proof of the splitting principle for oriented vector bundles

Jack LeeI'm trying to understand the proof of the following result in Lawson & Michelsohn's Spin Geometry: Proposition 11.2. Let $E$ be an oriented real vector bundle of dimension $2n$ over a manifold $X$. Then there is a smooth proper fibration $\pi\colon \mathscr S_E\to X$ such that $\pi^*\colon H^*(X...

 

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