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 –coefficients, where is the localized ring at 2.
"Properties of Bott manifolds and cohomological rigidity." Algebr. Geom. Topol. 11 (2) 1053 - 1076, 2011. https://doi.org/10.2140/agt.2011.11.1053