The categorical automorphism group of the strict Lie 2-group classifying topological T-duality correspondences is a non-central categorical extension of the integral split pseudo-orthogonal group that splits over several subgroups and has 2-torsion k-invariant.
T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
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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 "non-classical," 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 non-classical 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 non-uniqueness of T-duals can be studied via the action of the T-duality group.
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Categorical symmetries of T-duality
The categorical automorphism group of the strict Lie 2-group classifying topological T-duality correspondences is a non-central categorical extension of the integral split pseudo-orthogonal group that splits over several subgroups and has 2-torsion k-invariant.