Cohomological non-rigidity of generalized real Bott manifolds of height 2

Details Cohomological non-rigidity of generalized real Bott manifolds of height 2 Cohomological non-rigidity of generalized real Bott manifolds of height 2

2008-09-12

arxiv.org/abs/0809.2215v2

Proceedings of the Steklov Institute of Mathematics, 2010, Vol. 268, pp. 242-247

Mathematics

Algebraic Topology

Scientific paper

10.1134/S0081543810010165

We investigate when two generalized real Bott manifolds of height 2 have isomorphic cohomology rings with Z/2 coefficients and also when they are diffeomorphic. It turns out that cohomology rings with Z/2 coefficients do not distinguish those manifolds up to diffeomorphism in general. This gives a counterexample to the cohomological rigidity problem for real toric manifolds posed in \cite{ka-ma08}. We also prove that generalized real Bott manifolds of height 2 are diffeomorphic if they are homotopy equivalent.

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