Geodesic
Cohomological non-rigidity of generalized real Bott manifolds of height~2
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. I, Tome 268 (2010), pp. 252-257

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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. 
@article{TM_2010_268_a15,
     author = {M. Masuda},
     title = {Cohomological non-rigidity of generalized real {Bott} manifolds of height~2},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {252--257},
     publisher = {mathdoc},
     volume = {268},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_268_a15/}
}
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M. Masuda. Cohomological non-rigidity of generalized real Bott manifolds of height~2. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. I, Tome 268 (2010), pp. 252-257. http://geodesic.mathdoc.fr/item/TM_2010_268_a15/