Abstract
AbstractTopological T-duality is a relationship between pairs (E, P) over a fixed space X, where $$E \rightarrow X$$
E
→
X
is a principal torus bundle and $$P \rightarrow E$$
P
→
E
is a twist, such as a gerbe for a principal $$PU({\mathcal {H}})$$
P
U
(
H
)
-bundle. This is of interest to topologists because of the T-duality transformation: a T-duality relation between pairs (E, P) and $$({\hat{E}}, {\hat{P}})$$
(
E
^
,
P
^
)
comes with an isomorphism (with degree shift) between the twisted K-theory of E and the twisted K-theory of $${\hat{E}}$$
E
^
. We formulate topological T-duality for circle bundles in the equivariant setting, following the definition of Bunke, Rumpf, and Schick. We define the T-duality transformation in equivariant K-theory and show that it is an isomorphism for all compact Lie groups, equal to its own inverse and uniquely characterized by naturality and a normalization for trivial situations.
Funder
German Academic Exchange Service
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
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