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1. • CommentRowNumber1.
   • CommentAuthorBruce Bartlett
   • CommentTimeOct 2nd 2013
   • PermaLink
   Author: Bruce Bartlett
   Format: MarkdownItexI 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?

   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?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 2nd 2013
   • (edited Oct 2nd 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexHey 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 _[[schreiber:Local prequantum field theory]]_. I have also just added a few remarks on this to _[[secondary invariant]]_ in the section _[Higher order invariants and boundary field theory](http://ncatlab.org/nlab/show/secondary+characteristic+class#HigherOrderInvariantsAndBoundaryFieldTheory)_.

   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.