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Cohomological rigidity of
real Bott manifolds
Yoshinobu Kamishima and Mikiya Masuda |
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Algebraic & Geometric Topology 9 (2009) 2479–2502
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Abstract |
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A real Bott manifold is the total space of an iterated –bundle over a point, where each –bundle is the projectivization of a Whitney sum of two real line bundles. We prove that two real Bott manifolds are diffeomorphic if their cohomology rings with –coefficients are isomorphic. A real Bott manifold is a real toric manifold and admits a flat Riemannian metric invariant under the natural action of an elementary abelian 2–group. We also prove that the converse is true, namely a real toric manifold which admits a flat Riemannian metric invariant under the action of an elementary abelian 2–group is a real Bott manifold. |
Keywords
real toric manifold, real Bott tower, flat Riemannian
manifold
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Mathematical Subject Classification 2000
Primary: 57R91
Secondary: 53C25, 14M25
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References |
Publication
Received: 28 August 2009
Accepted: 12 October 2009
Published: 13 December 2009
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Authors |
| Yoshinobu Kamishima | |
| Department of Mathematics Tokyo Metropolitan University Minami-Ohsawa 1-1 Hachioji Tokyo 192-0397 Japan |
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| Mikiya Masuda | |
| Department of Mathematics Osaka City University Sumiyoshi-ku Osaka 558-8585 Japan |
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