Algebraic & Geometric Topology 11 (2011) 1053–1076

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

Keywords

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

Mathematical Subject Classification

Primary: 57S25

Secondary: 22F30

References

Publication

Received: 24 April 2010
Revised: 31 October 2010
Accepted: 3 January 2011
Published: 30 March 2011

Authors