TOPOLOGICAL CLASSIFICATION OF GENERALIZED BOTT TOWERS

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If B is a toric manifold and E is a Whitney sum of complex line bundles over B, then the projectivization P(E) of E is again a toric manifold. Starting with B as a point and repeating this construction, we obtain a sequence of complex projective bundles which we call a generalized Bott tower. We prove that if the top manifold in the tower has the same cohomology ring as a product of complex projective spaces, then every fibration in the tower is trivial so that the top manifold is diffeomorphic to the product of complex projective spaces. This gives supporting evidence to what we call the cohomological rigidity problem for tone manifolds, "Are toric manifolds diffeomorphic (or homeomorphic) if their cohomology rings are isomorphic?" We provide two more results which support the cohomological rigidity problem.
Publisher
AMER MATHEMATICAL SOC
Issue Date
2010-02
Language
English
Article Type
Article
Keywords

TORIC MANIFOLDS

Citation

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.362, no.2, pp.1097 - 1112

ISSN
0002-9947
URI
http://hdl.handle.net/10203/98456
Appears in Collection
MA-Journal Papers(저널논문)
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