  Topological T-duality is a relationship between pairs (E, P ) over a fixed
space X, where E over X is a principal torus bundle and P over E is a twist,
such as a gerbe of principal PU(H)-bundle. This is of interest to topologists
because of the T-duality transformation: a T-duality relation between pairs (E,
P ) and (F, Q ) comes with an isomorphism (with degree shift) between the
twisted K-theory of E and the twisted K-theory of F. We formulate topological
T-duality 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 actions of compact Lie groups, equal to its
own inverse and uniquely characterized by naturality and a normalization for
trivial situations.
