Geodesic
Cohomological non-rigidity of generalized real Bott manifolds of height 2
Informatics and Automation, Differential equations and topology. I, Tome 268 (2010), pp. 252-257 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the following problem: When do two generalized real Bott manifolds of height 2 have isomorphic cohomology rings with $\mathbb Z/2$ coefficients and also when are they diffeomorphic? It turns out that in general cohomology rings with $\mathbb Z/2$ coefficients do not distinguish those manifolds up to diffeomorphism. This gives a negative answer to the cohomological rigidity problem for real toric manifolds posed earlier by Y. Kamishima and the present author. We also prove that generalized real Bott manifolds of height 2 are diffeomorphic if they are homotopy equivalent. 
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M. Masuda. Cohomological non-rigidity of generalized real Bott manifolds of height 2. Informatics and Automation, Differential equations and topology. I, Tome 268 (2010), pp. 252-257. http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a15/

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