26. Bundle-valued forms
In this lecture we generalise differential forms by allowing them to take values in a vector space (these are called vector-valued forms), or a vector bundle (these are called bundle-valued forms).
We then focus on the case of vector-valued forms on a principal bundle, and show that vector-valued forms that are both horizontal and equivariant can be identified with bundle-valued forms on the associated vector bundle.
The main application of this result will come next semester (as we will see, the curvature of a connection on a principal bundle satisfies these hypotheses).
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