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Associated to a differential character is an integral cohomology class,referred to as the characteristic class, and a closed differential form,referred to as the curvature. The characteristic class and curvature are equalin de Rham cohomology, and this is encoded in a commutative square. In theHopkins--Singer model, where differential characters are equivalence classes ofdifferential cocycles, there is a natural notion of trivializing a differentialcocycle. In this paper, we extend the notion of characteristic class,curvature, and de Rham class to trivializations of differential cocycles. Thesestructures fit into a commutative square, and this square is a torsor for thecommutative square associated to characters with degree one less. Under thecorrespondence between degree 2 differential cocycles and principal circlebundles with connection, we recover familiar structures associated to globalsections.

Trivializations of differential cocycles