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 via noncommutative topology
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
It is known that the T-dual of a circle bundle with H-flux (given by a Neveu-Schwarz 3-form) is the T-dual circle bundle with dual H-flux. However, it is also known that torus bundles with H-flux do not necessarily have a T-dual which is a torus bundle. A big puzzle has been to explain these mysterious "missing T-duals.'' Here we show that this problem is resolved using noncommutative topology. It turns out that every principal 2-torus-bundle with H-flux does indeed have a T-dual, but in the missing cases (which we characterize), the T-dual is non-classical and is a bundle of noncommutative tori. The duality comes with an isomorphism of twisted K-theories, just as in the classical case. The isomorphism of twisted cohomology which one gets in the classical case is replaced by an isomorphism of twisted cyclic homology.
fields
math.AT 1years
2022 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
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.