Abstract: A Bott tower is a sequence B_n --> B_{n-1}-->...--> B_1--> B_0 where B_0
is a point and Bi is a CP1-bundle over B{i-1} for i = 1... n. Each B_i is a called the i-th stage Bott manifold. One can extend this de nition to define a generalized Bott tower and manifold to be a sequence of complex space bundles. One of the interesting question in toric topology asks whether two (generalized) Bott manifolds B_n and B_n^' are homeomorphic (or diffeomorphic) provided their cohomologies are isomorphic as graded rings. This is called the cohomological rigidity question for(generalized) Bott manifolds. In this talk we discuss some related back ground material from toric theory and some positive results on the question.
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Bott_Manifold_andCohomological_Rigidity.pdf