Algebraic & Geometric Topology

Cohomological rigidity of real Bott manifolds

Yoshinobu Kamishima and Mikiya Masuda

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A real Bott manifold is the total space of an iterated 1–bundle over a point, where each 1–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 2–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.

Article information

Algebr. Geom. Topol., Volume 9, Number 4 (2009), 2479-2502.

Received: 28 August 2009
Accepted: 12 October 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R91: Equivariant algebraic topology of manifolds
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 14M25: Toric varieties, Newton polyhedra [See also 52B20]

real toric manifold real Bott tower flat Riemannian manifold


Kamishima, Yoshinobu; Masuda, Mikiya. Cohomological rigidity of real Bott manifolds. Algebr. Geom. Topol. 9 (2009), no. 4, 2479--2502. doi:10.2140/agt.2009.9.2479.

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