Properties of Bott manifolds and cohomological rigidity

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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((2))-coefficients, where Z((2)) is the localized ring at 2.
Publisher
GEOMETRY TOPOLOGY PUBLICATIONS
Issue Date
2011
Language
English
Article Type
Article
Keywords

CONVEX POLYTOPES; CLASSIFICATION; TOWERS

Citation

ALGEBRAIC AND GEOMETRIC TOPOLOGY, v.11, no.2, pp.1053 - 1076

ISSN
1472-2739
URI
http://hdl.handle.net/10203/95924
Appears in Collection
MA-Journal Papers(저널논문)
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