Algebraic & Geometric Topology

Properties of Bott manifolds and cohomological rigidity

Suyoung Choi and Dong Youp Suh

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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.

Article information

Source
Algebr. Geom. Topol., Volume 11, Number 2 (2011), 1053-1076.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715219

Digital Object Identifier
doi:10.2140/agt.2011.11.1053

Mathematical Reviews number (MathSciNet)
MR2792373

Zentralblatt MATH identifier
1238.57032

Subjects
Primary: 57S25: Groups acting on specific manifolds
Secondary: 22F30: Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40}

Keywords
toric manifold quasitoric manifold Bott tower twist number cohomological complexity cohomological rigidity one-twisted Bott tower

Citation

Choi, Suyoung; Suh, Dong Youp. Properties of Bott manifolds and cohomological rigidity. Algebr. Geom. Topol. 11 (2011), no. 2, 1053--1076. doi:10.2140/agt.2011.11.1053. https://projecteuclid.org/euclid.agt/1513715219


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