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    • CommentRowNumber1.
    • CommentAuthorBruce Bartlett
    • CommentTimeOct 2nd 2013

    I saw an interesting article on the arXiv today:

    Iyer, Tertiary classes for a one-parameter variation of flat connections on a smooth manifold,

    I wonder how this ties in with Urs’s viewpoint of differential cohomology?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 2nd 2013
    • (edited Oct 2nd 2013)

    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.