Discrete Group Actions and Generalized Real Bott Manifolds
نویسندگان
چکیده
منابع مشابه
Classification of Real Bott Manifolds
A real Bott manifold is the total space of a sequence of RP 1 bundles starting with a point, where each RP 1 bundle is the projectivization of a Whitney sum of two real line bundles. A real Bott manifold is a real toric manifold which admits a flat riemannian metric. An upper triangular (0, 1) matrix with zero diagonal entries uniquely determines such a sequence of RP 1 bundles but different ma...
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Abstract. A real Bott manifold is the total space of iterated RP 1 bundles starting with a point, where each RP 1 bundle is projectivization of a Whitney sum of two real line bundles. We prove that two real Bott manifolds are diffeomorphic if their cohomology rings with Z/2 coefficients are isomorphic. A real Bott manifold is a real toric manifold and admits a flat riemannian metric invariant u...
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We construct two classes of examples of a virtually torsionfree group G acting properly and cocompactly on a contractible manifold X. In the first class of examples the universal space for proper actions, EG, has no model with finitely many orbits of cells. The reason is that the centralizers of certain finite subgroups of G will not have finitetype classifying spaces. In the second class of ex...
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We completely characterize real Bott manifolds up to diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously. We also prove that any graded ring isomorphism between the cohomology rings of real Bott manifolds with Z/2 coefficients is induced by an affine diffeomorphism betwe...
متن کاملCohomological Non-rigidity of Generalized Real Bott Manifolds of Height 2
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 [5]. We als...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2011
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2011.v18.n6.a17