Abstract. A complex projective tower or simply a CP -tower is an iterated complex projective fibrations starting from a point. In this paper we classify all 6-dimensional CP -towers up to diffeomorphism, and as a consequence, we show that all such manifolds are cohomologically rigid, i.e., they are completely determined up to diffeomorphism by their cohomology rings. We also show that cohomological rigidity is not valid for 8-dimensional CP -towers by classifying some CP 1 -fibrations over CP 3 up to diffeomorphism. As a corollary we show that such CP -towers are diffeomorphic if they are homotopy equivalent.

No abstract

A complex projective tower or simply a CP-tower is an iterated complex projective fibrations starting from a point. In this paper we classify all 6-dimensional CP-towers up to diffeomorphism, and as a consequence, we show that all such manifolds are cohomologically rigid, i.e., they are completely determined up to diffeomorphism by their cohomology rings. Contents 1. Introduction 1 2. Some preliminaries 3 3. The class CPM 6 2 5 4. The class CPM 6 3 8 Acknowledgments 20 References 20