Volume 15, issue 2 (2015)

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Cohomological non-rigidity of eight-dimensional complex projective towers

Shintarô Kuroki and Dong Youp Suh

Algebraic & Geometric Topology 15 (2015) 769–782
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.

Keywords
complex projective bundles, cohomological rigidity problem, toric topology
Primary: 57R22
Secondary: 57S25