---
abstract: 'The cohomological rigidity problem for toric manifolds asks whether the cohomology ring of a toric manifold determines the topological type of the manifold. In this paper, we consider the problem with the class of one-twist Bott manifolds to get an affirmative answer to the problem. We also generalize the result to quasitoric manifolds. In doing so, we show that the twist number of a Bott manifold is well-defined and is equal to the cohomological complexity of the cohomology ring of the manifold. We also show that any cohomology Bott manifold is homeomorphic to a Bott manifold. All these results are also generalized to the case with ${\mathbb{Z}}_{(2)}$-coefficients, where ${\mathbb{Z}}_{(2)}$ is the localized ring at $2$.'
address:
- 'Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan'
- 'Department of Mathematical Sciences, KAIST, 335 Gwahangno, Yu-sung Gu, Daejeon 305-701, Korea'
author:
- Suyoung Choi
- Dong Youp Suh
title: Properties of Bott manifolds and Cohomological Rigidity
---

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Introduction
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A class $\mathcal M$ of closed manifolds is said to be [*cohomologically rigid*]{} if any two elements $M,N\in \mathcal M$ are homeomorphic whenever their cohomology rings are isomorphic. One of the intersting problems in toric topology 