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arXiv · 0809.2215

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

Mikiya Masuda
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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 \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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Mikiya Masuda. 2008-09-23. Cohomological non-rigidity of generalized real Bott manifolds of height 2. https://doi.org/10.1134/s0081543810010165

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