Strong cohomological rigidity conjecture for Bott manifolds

A Bott tower of height $n$ is an iterated $\mathbb C P^1$-bundle whose stages are Bott manifolds; each Bott manifold is a closed manifold of dimension $2n$. Strong cohomological rigidity conjecture. Any graded ring isomorphism between the cohomology rings of two Bott manifolds is induced by a diffeomorphism. This conjecture concerns whether the cohomology ring determines the diffeomorphism type of a Bott manifold. The paper establishes the conjecture for Bott manifolds of dimension $8$ as a corollary of its main theorem, while the general case is not resolved here.