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arXiv:1208.3961 Differential cohomology from arXiv Front: math.AT by Ulrich Bunke These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of generalized cohomology theories including products and Umkehr maps.
Axiomatic characterization of ordinary differential cohomology. James Simons and Dennis Sullivan, in Journal of Topology.
nLab on differential cohomology
[arXiv:1211.6832] A Bicategory Approach to Differential Cohomology from arXiv Front: math.AT by Markus Upmeier A very natural bicategory approach to differential cohomology is presented. Based on the axioms of Bunke-Schick, a symmetric monoidal groupoid is associated to any differential cohomology theory. The main result is then that such a differential refinement is unique up to equivalence of the corresponding symmetric monoidal groupoids. The uniqueness results for rationally-even theories are interpreted in this framework. Moreover, we show how the bicategory formalism may be used to give a simple construction of a differential refinement for any generalized cohomology theory.
nLab page on Differential cohomology?
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