Volume 15, issue 2 (2015)

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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 $ℂ{ℙ}^{1}$–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 $ℤ∕2$–trivial, where a Bott manifold is called $ℤ∕2$–trivial if its cohomology ring with $ℤ∕2$–coefficients is isomorphic to that of a product of copies of $ℂ{ℙ}^{1}$.

Keywords
Bott manifold, cohomological rigidity, Pontrjagin class, torus manifold, $\mathbb{Z}_2$–trivial Bott manifold
Mathematical Subject Classification 2010
Primary: 57R19, 57R20
Publication
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