Prof. Dong Youp Suh,KAIST

Complex Projective Towers and Cohomological Rigidity Problem

A complex projective tower is a sequence of fibrations with complex projective spaces as fibers. Bott towers and generalized Bott towers are examples of complex projective towers. The cohomological rigidity question asks whether a certain class of manifolds is classified up to homeomorphism or diffeomorphism by their cohomology rings. In this lecture we would like to answer the question for the class of complex projective towers. The cohomological rigidity question is still open for Bott manifolds of generalized Bott manifolds, even though there are several cases with positive answers. In this lecture we classify all complex projective towers up to dimension 6 and show that the cohomological rigidity question has the positive answer for such subclass. On the other hand we show that there are two different complex projective towers of dimension 8 with the same cohomology rings, hence the cohomological rigidity is negative in general for complex projective towers. However these two manifolds have different homotopy groups.