A Cech Dimensionally Reduced Gysin Sequence for Principal Torus Bundles
  In this paper we construct Cech cohomology groups that form a Gysin-type long exact sequence for principal torus bundles. This sequence is modeled on a de Rham cohomology sequence published in earlier work by Bouwknegt, Hannabuss and Mathai, which was developed to compute the global properties of T-duality in the presence of NS H-Flux. 
Peter Bouwknegt and Rshni Ratnam
math.GT