Volume 15, issue 2 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Invariance of Pontrjagin classes for Bott manifolds

Suyoung Choi, Mikiya Masuda and Satoshi Murai

Algebraic & Geometric Topology 15 (2015) 965–986
Abstract

A Bott manifold is the total space of some iterated 1–bundles over a point. We prove that any graded ring isomorphism between the cohomology rings of two Bott manifolds preserves their Pontrjagin classes. Moreover, we prove that such an isomorphism is induced from a diffeomorphism if the Bott manifolds are 2–trivial, where a Bott manifold is called 2–trivial if its cohomology ring with 2–coefficients is isomorphic to that of a product of copies of 1.

Keywords
Bott manifold, cohomological rigidity, Pontrjagin class, torus manifold, $\mathbb{Z}_2$–trivial Bott manifold
Mathematical Subject Classification 2010
Primary: 57R19, 57R20
References
Publication
Received: 6 May 2014
Revised: 15 September 2014
Accepted: 18 September 2014
Published: 22 April 2015
Authors
Suyoung Choi
Department of Mathematics
Ajou University
San 5, Woncheon-dong, Yeongtong-gu
Suwon 443-749
South Korea
Mikiya Masuda
Department of Mathematics
Osaka City University
3-3-138, Sugimoto, Sumiyoshi-ku
Osaka-shi 558-8585
Japan
Satoshi Murai
Department of Pure and Applied Mathematics
Graduate School of Information Science and Technology
Osaka University
Toyonaka
Osaka 560-0043
Japan