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I saw an interesting article on the arXiv today:
Iyer, Tertiary classes for a one-parameter variation of flat connections on a smooth manifold, http://arxiv.org/abs/1310.0001.
I wonder how this ties in with Urs’s viewpoint of differential cohomology?
Hey Bruce,
thanks for alerting me. That article effectively discusses transgression of differential cocycles by fiber integration in ordinary differential cohomology.
There is a whole tower of “higher order invariants” obtained this way by iterative transgression. We may call them:
primary invariants: topological Yang-Mills terms;
secondary invariants: Chern-Simons terms;
ternary invariants: WZW terms;
quaternary invariants: Wilson loop terms.
This is discussed in some detail at Local prequantum field theory (schreiber). I have also just added a few remarks on this to secondary invariant in the section Higher order invariants and boundary field theory.
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