  We reexamine the results on the global properties of T-duality for principal
circle bundles in the context of a dimensionally reduced Gysin sequence. We
will then construct a Gysin sequence for principal torus bundles and examine
the consequences. In particular, we will argue that the T-dual of a principal
torus bundle with nontrivial H-flux is, in general, a continuous field of
noncommutative, nonassociative tori.
