Topological classification of generalized Bott towers
Topological classification of generalized Bott towers
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DOI：
10.1090/s0002-9947-09-04970-8
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发表时间：
2008-07
影响因子：
1.3
通讯作者：
Suyoung Choi;M. Masuda;D. Suh
中科院分区：
文献类型：
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作者：
Suyoung Choi;M. Masuda;D. Suh
若B是环面流形，E是B上复线丛的Whitney和，则E的射影化P（E）又是环面流形。从B作为一个点开始，重复这个构造，我们得到一个复射影丛序列，我们称之为广义Bott塔。证明了如果塔中的顶流形具有与复射影空间的乘积相同的上同调环，则塔中的每一纤维化都是平凡的，使得顶流形是复射影空间的乘积的非纯的.这为我们所说的复曲面流形的上同调刚性问题提供了支持证据，“如果复曲面流形的上同调环是同构的，那么它们是微分同胚（或同胚）的吗？“我们提供了两个支持上同调刚性问题的结果。
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 toric manifolds, "Are toric manifolds diffeomorphic (or homeomorphic) if their cohomology rings are isomorphic?" We provide two more results which support the cohomological rigidity problem.