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December 2014 T-duality for circle bundles via noncommutative geometry
Varghese Mathai, Jonathan Rosenberg
Adv. Theor. Math. Phys. 18(6): 1437-1462 (December 2014).


Recently Baraglia showed how topological T-duality can be extended to apply not only to principal circle bundles, but also to non-principal circle bundles. We show that his results can also be recovered via two other methods: the homotopy-theoretic approach of Bunke and Schick, and the noncommutative geometry approach which we previously used for principal torus bundles. This work has several interesting byproducts, including a study of the $K$-theory of crossed products by $\tilde{O}(2) = \mathrm{Isom}(\mathbb{R})$, the universal cover of $O(2)$, and some interesting facts about equivariant $K$-theory for $\mathbb{Z}/ 2$. In the final section of this paper, some of these results are extended to the case of bundles with singular fibers, or in other words, non-free $O(2)$-actions.


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Varghese Mathai. Jonathan Rosenberg. "T-duality for circle bundles via noncommutative geometry." Adv. Theor. Math. Phys. 18 (6) 1437 - 1462, December 2014.


Published: December 2014
First available in Project Euclid: 4 December 2014

zbMATH: 1308.81149
MathSciNet: MR3285613

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 6 • December 2014
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