7:40 PM
6

I'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...