## Osaka Journal of Mathematics

### $\mathbb{Q}$-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.

#### Article information

Source
Osaka J. Math., Volume 51, Number 4 (2014), 1081-1093.

Dates
First available in Project Euclid: 31 October 2014

https://projecteuclid.org/euclid.ojm/1414761912

Mathematical Reviews number (MathSciNet)
MR3273878

Zentralblatt MATH identifier
1311.57049

#### Citation

Park, Seonjeong; Suh, Dong Youp. $\mathbb{Q}$-trivial generalized Bott manifolds. Osaka J. Math. 51 (2014), no. 4, 1081--1093. https://projecteuclid.org/euclid.ojm/1414761912

#### References

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