논문
Q-trivial generalized Bott manifolds
- 저자Seonjeong Park and Dong Youp Suh
- 학술지Osaka J. Math. 51
- 등재유형
- 게재일자(2014)
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.
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.
