Cohomological rigidity of real Bott manifolds

Details Cohomological rigidity of real Bott manifolds Cohomological rigidity of real Bott manifolds

2008-07-26

arxiv.org/abs/0807.4263v1

Algebr. Geom. Topol. 9 (2009), 2479-2502

Mathematics

Algebraic Topology

22 pages

Scientific paper

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.

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