Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 9, Number 4 (2009), 2479-2502.
Cohomological rigidity of real Bott manifolds
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.
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
Permanent link to this document
Digital Object Identifier
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]
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