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2011 Properties of Bott manifolds and cohomological rigidity
Suyoung Choi, Dong Youp Suh
Algebr. Geom. Topol. 11(2): 1053-1076 (2011). DOI: 10.2140/agt.2011.11.1053

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 (2)–coefficients, where (2) is the localized ring at 2.

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Suyoung Choi. Dong Youp Suh. "Properties of Bott manifolds and cohomological rigidity." Algebr. Geom. Topol. 11 (2) 1053 - 1076, 2011. https://doi.org/10.2140/agt.2011.11.1053

Information

Received: 24 April 2010; Revised: 31 October 2010; Accepted: 3 January 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1238.57032
MathSciNet: MR2792373
Digital Object Identifier: 10.2140/agt.2011.11.1053

Subjects:
Primary: 57S25
Secondary: 22F30

Rights: Copyright © 2011 Mathematical Sciences Publishers

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Vol.11 • No. 2 • 2011
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