Classification of Q-trivial Bott manifolds
Abstract
A Bott manifold is a closed smooth manifold obtained as the total space of an iterated P1-bundle starting with a point, where each P1-bundle is the projectivization of a Whitney sum of two complex line bundles. A -trivial Bott manifold of dimension 2n is a Bott manifold whose cohomology ring is isomorphic to that of (1)n with -coefficients. We find all diffeomorphism types of -trivial Bott manifolds and show that they are distinguished by their cohomology rings with -coefficients. As a consequence, we see that the number of diffeomorphism classes in -trivial Bott manifolds of dimension 2n is equal to the number of partitions of n. We even show that any cohomology ring isomorphism between two -trivial Bott manifolds is induced by a diffeomorphism.