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Properties of Bott
manifolds and cohomological rigidity
Suyoung Choi and Dong Youp Suh |
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Algebraic & Geometric Topology 11 (2011) 1053–1076
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Abstract |
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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 –coefficients, where is the localized ring at 2. |
Keywords
toric manifold, quasitoric manifold, Bott tower, twist
number, cohomological complexity, cohomological rigidity,
one-twisted Bott tower
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Mathematical Subject Classification 2000
Primary: 57S25
Secondary: 22F30
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References |
Publication
Received: 24 April 2010
Revised: 31 October 2010
Accepted: 3 January 2011
Published: 30 March 2011
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Authors |
| Suyoung Choi | |
| Department of Mathematics Ajou University San 5 Woncheon-dong Yeongtong-gu Suwon 443-749 Republic of Korea |
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| Dong Youp Suh | |
| Department of Mathematical
Sciences KAIST 335 Gwahangno Yu-sung Gu Daejeon 305-701 Republic of Korea |
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