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Invariance of
Pontrjagin classes for Bott manifolds
Suyoung Choi, Mikiya Masuda and Satoshi Murai |
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Algebraic & Geometric Topology 15 (2015) 965–986
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Abstract |
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A Bott manifold is the total space of some iterated –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 –trivial, where a Bott manifold is called –trivial if its cohomology ring with –coefficients is isomorphic to that of a product of copies of . |
Keywords
Bott manifold, cohomological rigidity, Pontrjagin class,
torus manifold, $\mathbb{Z}_2$–trivial Bott manifold
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Mathematical Subject Classification 2010
Primary: 57R19, 57R20
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References |
Publication
Received: 6 May 2014
Revised: 15 September 2014
Accepted: 18 September 2014
Published: 22 April 2015
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Authors |
| Suyoung Choi | |
| Department of Mathematics Ajou University San 5, Woncheon-dong, Yeongtong-gu Suwon 443-749 South Korea |
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| Mikiya Masuda | |
| Department of Mathematics Osaka City University 3-3-138, Sugimoto, Sumiyoshi-ku Osaka-shi 558-8585 Japan |
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| Satoshi Murai | |
| Department of Pure and Applied
Mathematics Graduate School of Information Science and Technology Osaka University Toyonaka Osaka 560-0043 Japan |
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