## Algebraic & Geometric Topology

### Cohomological rigidity of real Bott manifolds

#### Abstract

A real Bott manifold is the total space of an iterated $ℝℙ1$–bundle over a point, where each $ℝℙ1$–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 $ℤ∕2$–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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513797090

Digital Object Identifier
doi:10.2140/agt.2009.9.2479

Mathematical Reviews number (MathSciNet)
MR2576506

Zentralblatt MATH identifier
1195.57071

#### Citation

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. https://projecteuclid.org/euclid.agt/1513797090

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