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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 30th 2011

    this here is more a remark to myself, for tomorrow morning. But maybe somebody finds it to be of interest (or else, can tell me what’s wrong with it ;-)

    With Domenico Fiorenza I once made some notes at T-Duality and Differential K-Theory, observing that the “differential T-duality pairs” introduced by Kahle and Valentino (following Freed) are really examples of twisted differential structures, where there twisting cocycle is in this case the cup product of two Chern-classes of two tori.

    Now, there is a very obvious remark that needs to follow this remark:

    this says that the volume holomomy functional of the “twisting line 3-bundles” in this case of differential T-duality is nothing but… torus-Chern-Simons-theory! (By the logic that I have currently spelled out only at higher dimensional Chern-Simons theory): the integral over the cup product in ordinary differential cohomology of the two torus connections.

    This needs to be followed-up by something. Something important is happening here. I need to understand this.