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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 30th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexthis 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.

   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.