Axiomatic Characterization of Ordinary Differential Cohomology

Ĥ satisfies the Character Diagram shown in §1 and thus has natural transformations onto both closed differential forms with integral periods and integral cohomology. It was shown in [6] that an enriched version of the Weil homomorphism, carrying both an invariant polynomial and an associated integral homology class of the classifying space, naturally factors through Ĥ on its way to these targets. Based on this and other considerations, Ĥ has been shown to have useful applications to a number of areas, including conformal geometry and flat bundles. Most recently, the characters, perhaps generalized to relate to K-theory, have appeared in descriptions of quantizations of field theory related to super gravity and string theory, cf. [14].