## Algebraic & Geometric Topology

### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 15, Number 2 (2015), 769-782.

Dates
Revised: 25 July 2014
Accepted: 12 January 2015
First available in Project Euclid: 28 November 2017

https://projecteuclid.org/euclid.agt/1511895788

Digital Object Identifier
doi:10.2140/agt.2015.15.769

Mathematical Reviews number (MathSciNet)
MR3342675

Zentralblatt MATH identifier
1320.57033

#### Citation

Kuroki, Shintarô; Suh, Dong Youp. Cohomological non-rigidity of eight-dimensional complex projective towers. Algebr. Geom. Topol. 15 (2015), no. 2, 769--782. doi:10.2140/agt.2015.15.769. https://projecteuclid.org/euclid.agt/1511895788

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