Abstract
In string theory, the concept of T-duality between two principal U(1)-bundles E_1 and E_2 over the same base space B, together with cohomology classes
h
1
∈
H
3
(
E
1
)
and
h
2
∈
H
3
(
E
2
)
, has been introduced. One of the main virtues of T-duality is that
h
1
-twisted K-theory of
E
1
is isomorphic to
h
2
-twisted K-theory of
E
2
. In this paper, a new, very topological concept of T-duality is introduced. The study pairs (E,h) as above from a topological point of view and construct a classifying space of such pairs. Using this, we construct a universal dual pair to a given pair. Our construction immediately gives a number of known and new properties of the dual. In particular it implies existence of a dual of any pair (E,h), and it also describes the ambiguity upto which the dual is well defined. In order to deal with twisted K-theory, some care is needed, in particular when dealing with naturality questions, because the twisted K-theory depends on the explicit model for the twists and the twisted theory --care which is missing in some of the existing literature. We illustrate the use of T-duality by some explicit calculations of twisted K-groups.