orientation in differential cohomology in nLab

Contents

Contents

Idea

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.

Examples

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

References

Around def. 4.19 in

• Mike Hopkins, Isadore Singer, Quadratic Functions in Geometry, Topology, and M-Theory