Cohomological non-rigidity of eight-dimensional complex projective towers

Abstract

A complex projective tower, or simply CP tower, is an iterated complex projective fibration starting from a point. In this paper, we classify a certain class of 8-dimensional CP towers up to diffeomorphism. As a consequence, we show that cohomological rigidity is not satisfied by the collection of 8-dimensional CP towers: there are two distinct 8-dimensional CP towers that have the same cohomology rings.