A Bott manifold is the total space of some iterated ℂℙ1 –bundles over a point. We prove that any graded ring isomorphism between the cohomology rings of two Bott manifolds preserves their Pontrjagin classes. Moreover, we prove that such an isomorphism is induced from a diffeomorphism if the Bott manifolds are ℤ/2– trivial, where a Bott manifold is called ℤ/2–trivial if its cohomology ring with ℤ/2–coefficients is isomorphic to that of a product of copies of ℂℙ1.
ASJC Scopus subject areas
- Geometry and Topology