Cohomological non-rigidity of generalized real Bott manifolds of height 2
Abstract
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 ka-ma08. We also prove that generalized real Bott manifolds of height 2 are diffeomorphic if they are homotopy equivalent.
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