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.