Properties of Bott manifolds and cohomological rigidity

Choi, Suyoung¹ ; Suh, Dong Youp²

¹Department of Mathematics, Ajou University, San 5, Woncheon-dong, Yeongtong-gu, Suwon 443-749, Republic of Korea
²Department of Mathematical Sciences, KAIST, 335 Gwahangno, Yu-sung Gu, Daejeon 305-701, Republic of Korea

Algebraic and Geometric Topology, Tome 11 (2011) no. 2, pp. 1053-1076

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.1053

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

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