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arXiv · 1306.4198

T-duality for circle bundles via noncommutative geometry

Varghese Mathai·Jonathan Rosenberg
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Abstract

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 Isom(R), the universal cover of O(2), and some interesting facts about equivariant K-theory for Z/2. In the final section of this paper, 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. 2014-01-31. T-duality for circle bundles via noncommutative geometry. https://doi.org/10.4310/atmp.2014.v18.n6.a6

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