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January 2006 $T$-duality for torus bundles with $H$-fluxes via noncommutative topology. II. The high-dimensional case and the $T$-duality group
Varghese Mathai, Jonathan Rosenberg
Adv. Theor. Math. Phys. 10(1): 123-158 (January 2006).

Abstract

We use noncommutative topology to study T-duality for principal torus bundles with H-flux. We characterize precisely when there is a "classical" T-dual, i.e., a dual bundle with dual H-flux, and when the T-dual must be "nonclassical," that is, a continuous field of noncommutative tori. The duality comes with an isomorphism of twisted $K$-theories, required for matching of D-brane charges, just as in the classical case. The isomorphism of twisted cohomology which one gets in the classical case is replaced in the nonclassical case by an isomorphism of twisted cyclic homology. An important part of the paper contains a detailed analysis of the classifying space for topological T-duality, as well as the T-duality group and its action. The issue of possible nonuniqueness of T-duals can be studied via the action of the T-duality group.

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Varghese Mathai. Jonathan Rosenberg. "$T$-duality for torus bundles with $H$-fluxes via noncommutative topology. II. The high-dimensional case and the $T$-duality group." Adv. Theor. Math. Phys. 10 (1) 123 - 158, January 2006.

Information

Published: January 2006
First available in Project Euclid: 30 July 2006

zbMATH: 1111.81131
MathSciNet: MR2222224

Subjects:
Primary: 81T30
Secondary: 58Bxx , 81R60

Rights: Copyright © 2006 International Press of Boston

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Vol.10 • No. 1 • January 2006
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