$\mathbb{Q}$-trivial generalized Bott manifolds

Abstract

When the cohomology ring of a generalized Bott manifold with $\mathbb{Q}$-coefficient is isomorphic to that of a product of complex projective spaces $\mathbb{C}{P}^{n_i}$, the generalized Bott manifold is said to be $\mathbb{Q}$-trivial. We find a necessary and sufficient condition for a generalized Bott manifold to be $\mathbb{Q}$-trivial. In particular, every $\mathbb{Q}$-trivial generalized Bott manifold is diffeomorphic to a ${\prod }_{n_i>1}\mathbb{C}{P}^{n_i}$-bundle over a $\mathbb{Q}$-trivial Bott manifold.

10 pages

Cited by in corpus (1)

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