Advances in Theoretical and Mathematical Physics

T-duality for circle bundles via noncommutative geometry

Varghese Mathai and 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 $\tilde{O}(2) = \mathrm{Isom}(\mathbb{R})$, 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.

Article information

Source
Adv. Theor. Math. Phys., Volume 18, Number 6 (2014), 1437-1462.

Dates
First available in Project Euclid: 4 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1417707823

Mathematical Reviews number (MathSciNet)
MR3285613

Zentralblatt MATH identifier
1308.81149

Citation

Mathai, Varghese; Rosenberg, Jonathan. T-duality for circle bundles via noncommutative geometry. Adv. Theor. Math. Phys. 18 (2014), no. 6, 1437--1462. https://projecteuclid.org/euclid.atmp/1417707823


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