We reexamine the effects of T-duality on the global properties for principal circle bundles in the context of a dimensionally reduced Gysin sequence. We then construct a Gysin sequence for principal torus bundles and examine the consequences. In particular, we argue that the T-dual of a principal torus bundle with nontrivial H-flux is, in general, a continuous field of noncommutative, nonassociative tori.
"T-duality for principal torus bundles and dimensionally reduced Gysin sequences." Adv. Theor. Math. Phys. 9 (5) 749 - 773, October 2005.