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

Keywords
complex projective bundles, cohomological rigidity problem, toric topology
Mathematical Subject Classification 2010
Primary: 57R22
Secondary: 57S25
References
Publication
Received: 30 November 2013
Revised: 25 July 2014
Accepted: 12 January 2015
Published: 22 April 2015
Authors
Shintarô Kuroki
Graduate School of Mathematical Sciences
University of Tokyo
3-8-1 Komaba Meguro-ku
Tokyo 153-8914
Japan
http://www.ms.u-tokyo.ac.jp/~kuroki/
Dong Youp Suh
Department of Mathematical Sciences
KAIST
335 Gwahangno, Yuseong Gu
Daejeon 305-701
South Korea