On the Classification of Cohomology Bott Manifolds

Abstract

We study cohomology Bott manifolds by means of modified surgery theory. Cohomology Bott manifolds admit a ring isomorphism to the cohomology ring of a Bott manifold which preserves the Pontrjagin and Stiefel-Whitney classes. We show that the number of diffeomorphism classes of cohomology Bott manifolds is finite and construct first examples of manifolds which are cohomology Bott manifolds but not Bott manifolds. Furthermore, we consider the strong cohomological rigidity problem, i.e. we examine the realisability question for an automorphism of the cohomology ring of a specific Bott manifold.