Cohomological rigidity of real Bott manifolds
Cohomological rigidity of real Bott manifolds
复制标题
DOI：
10.2140/agt.2009.9.2479
复制
发表时间：
2008-07
期刊：
影响因子：
--
通讯作者：
Y. Kamishima;M. Masuda
中科院分区：
文献类型：
--
作者：
Y. Kamishima;M. Masuda
一个真实的Bott流形是从一个点开始的迭代RP ^1丛的全空间，其中每个RP ^1丛是两个真实的线丛的Whitney和的投影化。证明了两个真实的Bott流形是同构的，如果它们的系数为Z/2的上同调环是同构的.一个真实的Bott流形是一个真实的Toric流形，并且在初等交换2-群的自然作用下允许一个平坦的黎曼度量不变量。我们还证明了相反的情形也成立，即在初等交换2-群作用下，允许平坦黎曼度量不变量的真实的环面流形是真实的Bott流形。
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 under the natural action of an elementary abelian 2-group. We also prove that the converse is true, namely a real toric manifold which admits a flat riemannian metric invariant under the action of an elementary abelian 2-group is a real Bott manifold.