# T-Duality via Gerby Geometry and Reductions

@article{Bunke2013TDualityVG, title={T-Duality via Gerby Geometry and Reductions}, author={Ulrich Bunke and Thomas Nickelsen Nikolaus}, journal={arXiv: Differential Geometry}, year={2013} }

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…

## 11 Citations

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### T-Duality for Langlands Dual Groups

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### Fourier-Mukai Transforms from T-Duality

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## References

SHOWING 1-10 OF 41 REFERENCES

### A Groupoid Approach to Noncommutative T-Duality

- Mathematics
- 2007

Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows…

### Topology and H-flux of T-dual manifolds.

- MathematicsPhysical review letters
- 2004

A general formula for the topology and H-flux of the T-dual of a type II compactification is presented, finding that the manifolds on each side of the duality are circle bundles whose curvatures are given by the integral of theDual H- flux over the dual circle.

### T-Duality: Topology Change from H-Flux

- Mathematics
- 2004

T-duality acts on circle bundles by exchanging the first Chern class with the fiberwise integral of the H-flux, as we motivate using E8 and also using S-duality. We present known and new examples…

### On the Topology of T-Duality

- Mathematics
- 2005

We study a topological version of the T-duality relation between pairs consisting of a principal U(1)-bundle equipped with a degree-three integral cohomology class. We describe the homotopy type of a…

### Periodic Twisted Cohomology and T-Duality

- Mathematics
- 2011

The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a…

### THE TOPOLOGY OF T-DUALITY FOR Tn-BUNDLES

- Mathematics
- 2006

In string theory, the concept of T-duality between two principal Tn-bundles E and E over the same base space B, together with cohomology classes h ∈ H3(E,ℤ) and ĥ ∈ H3(E,ℤ), has been introduced. One…

### Duality for topological abelian group stacks and T-duality

- Mathematics
- 2007

We extend Pontrjagin duality from topological abelian groups to certain locally compact group stacks. To this end we develop a sheaf theory on the big site of topological spaces S in order to prove…

### T-duality for principal torus bundles and dimensionally reduced Gysin sequences

- Mathematics
- 2004

We reexamine the results on the global properties of T-duality for principal circle bundles in the context of a dimensionally reduced Gysin sequence. We will then construct a Gysin sequence for…

### Sheaf theory for stacks in manifolds and twisted cohomology for S 1 -gerbes

- Mathematics
- 2007

In this paper we give a sheaf theory interpretation of the twisted cohomology of manifolds. To this end we develop a sheaf theory on smooth stacks. The derived push-forward of the constant sheaf with…