Complex Projective Towers and Their Cohomological Rigidity up to Dimension Six

Abstract

A complex projective tower, or simply a CP-tower, is an iterated complex projective fibration starting from a point. In this paper we classify all six-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.