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.