#### Volume 11, issue 2 (2011)

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Properties of Bott manifolds and cohomological rigidity

### Suyoung Choi and Dong Youp Suh

Algebraic & Geometric Topology 11 (2011) 1053–1076
##### Abstract

The cohomological rigidity problem for toric manifolds asks whether the integral 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 ${ℤ}_{\left(2\right)}$–coefficients, where ${ℤ}_{\left(2\right)}$ is the localized ring at 2.

##### Keywords
toric manifold, quasitoric manifold, Bott tower, twist number, cohomological complexity, cohomological rigidity, one-twisted Bott tower
Primary: 57S25
Secondary: 22F30