Advances in Theoretical and Mathematical Physics

T-duality for circle bundles via noncommutative geometry

Varghese Mathai and Jonathan Rosenberg

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 4 December 2014

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Mathai, Varghese; Rosenberg, Jonathan. T-duality for circle bundles via noncommutative geometry. Adv. Theor. Math. Phys. 18 (2014), no. 6, 1437--1462.

Export citation