09-15 Notes

Here we have still fixed a manifold \(X\), and principal \(G\)-bundle \(\pi:P\to X\) with associated vector bundle \(E\to X\).

We need to understand the local topology of the space \({\mathcal B}^p_k={\mathcal A}^p_k/{\mathcal G}^p_{k+1}\). The best hope we could have is