Cohomological rigidity of real Bott manifolds

Abstract

A real Bott manifold is the total space of an iterated RP 1 -bundle over a point, where each RP 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 Z=2-coefficients are isomorphic.