Cohomological non-rigidity of eight-dimensional complex projective towers

Kuroki, Shintarô; Suh, Dong Youp

doi:10.2140/agt.2015.15.769

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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

DOI: 10.2140/agt.2015.15.769

Abstract

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

Volume 15, issue 2 (2015)