Cohomological rigidity of real Bott manifolds

By Y. Kamishima, M. Masuda. 2008

58 citations recorded by the source corpus.

A real Bott manifold is the total space of iterated RP^1 bundles starting with a point, where each RP^1 bundle is projectivization of a Whitney sum of two real line bundles. We prove that two real Bott manifolds are diffeomorphic if their cohomology rings with Z/2 coefficients are isomorphic. A real Bott manifold is a real toric manifold and admits a flat riemannian metric invariant under the natural action of an elementary abelian 2-group. We also prove that the converse is true, namely a real toric manifold which admits a flat riemannian metric invariant under the action of an elementary abelian 2-group is a real Bott manifold.

View Paper: https://www.semanticscholar.org/paper/a434e8ccf0ab3881cc0af44164de53562fb1e85e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. M. Masuda
2. T. Panov
3. Suyoung Choi
4. V. Buchstaber
5. D. Suh
6. J. Grbić
7. Hiroaki Ishida
8. Frédéric Bosio

Citations in the corpus

• Toric topology (2012, background): “This rigidity problem is affirmatively solved for real Bott manifolds ([42],”
• Toric Topology (2012, background): “The family of real Bott manifolds is cohomologically rigid over Z2 by the result of Kamishima–Masuda [178] (see also [73]), but the family of generalised Bott manifolds is not [208].”
• Rigidity problems in toric topology: A survey (2011, background): “Because of this reason the cohomological rigidity problem for real toric manifolds was addressed with Z/2-coefficient in [29], and it is shown there that the problem is affirmative for real Bott manifolds, where a real Bott manifold is the real analogue of a Bott manifold obtained by replacing C in ”