T-Duality via Gerby Geometry and Reductions

  title={T-Duality via Gerby Geometry and Reductions},
  author={Ulrich Bunke and Thomas Nickelsen Nikolaus},
  journal={arXiv: Differential Geometry},
We consider topological T-duality of torus bundles equipped with S^{1}-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S^{1}-valued functions which are constant along the torus fibres. We observe that such a reduction is exactly the additional datum needed for the construction of a T-dual pair. We illustrate the theory by working out the example of the canonical lifting gerbe on a compact Lie group which is a torus bundles over the associated… 

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