orientation in differential cohomology

An orientation in generalized cohomology is a certain cohomology class. An **orientation in differential cohomology** (possibly shortened to somewhat cryptic *differential orientation*) is not just the orientation in the underlying generalized cohomology theory, but it has more structure, namely it is a refinement of the ordinary orientation class to a cocycle in the corresponding differential cohomology.

- For ordinary differential cohomology a differential orientation is a differential Thom class. See there for details.

Around def. 4.19 in

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