Classification of $Q$-trivial Bott manifolds
Suyoung Choi, Mikiya Masuda · Journal of Symplectic Geometry · 2012
A Bott manifold is a closed smooth manifold obtained as the total space of an iterated CP 1 -bundle starting with a point, where each CP 1bundle is the projectivization of a Whitney sum of two complex line bundles.A Q-trivial Bott manifold of dimension 2n is a Bott manifold whose cohomology ring is isomorphic to that of (CP 1 ) n with Q-coefficients.We find all diffeomorphism types of Q-trivial Bott manifolds and show that they are distinguished by their cohomology rings with Z-coefficients.As a consequence, the number of diffeomorphism classes of Q-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 Q-trivial Bott manifolds is induced by a diffeomorphism.