Algebraic & Geometric Topology 9 (2009) 2479–2502

DOI: 10.2140/agt.2009.9.2479

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.

Keywords

real toric manifold, real Bott tower, flat Riemannian manifold

Mathematical Subject Classification

Primary: 57R91

Secondary: 14M25, 53C25

References

Publication

Received: 28 August 2009
Accepted: 12 October 2009
Published: 13 December 2009

Authors