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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

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Conceptual definition of the extension of a connection to 1-forms

I have a question that arose while reading Milnor's "Characteristic Classes". I will use the notation from that book. Let $M$ be a smooth manifold and let $\zeta$ be a complex vector bundle on $M$. …
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