论文标题
复杂矢量捆绑包的拓扑分类超过$ 8 $ - 二维旋转$^{c} $歧管
Topological classification of complex vector bundles over $8$-dimensional spin$^{c}$ manifolds
论文作者
论文摘要
在本文中，复杂的矢量捆绑包$ r $超过$ 8 $二维旋转$^{c} $歧管是根据复杂矢量捆绑包的Chern类和歧管的共同体圈的分类，其中$ r = 3 $或$ 4 $。作为一个应用程序，我们得到了两个排名$ 3 $复杂的矢量捆绑包，超过$ 4 $二维的复杂射击射击空间$ \ c p^{4} $是同构的，并且仅当它们具有相同的Chern类时。此外，确定了$ 3 $ 3 $复杂的向量捆绑包的Chern类超过$ \ c p^{4} $。将托马斯（Thomas）和斯威策（Switzer）的结果梳理到我们的工作中，我们可以断言，复杂的向量捆绑包在$ \ c p^{4} $上都被分类。
In this paper, complex vector bundles of rank $r$ over $8$-dimensional spin$^{c}$ manifolds are classified in terms of the Chern classes of the complex vector bundles and the cohomology ring of the manifolds, where $r = 3$ or $4$. As an application, we got that two rank $3$ complex vector bundles over $4$-dimensional complex projective spaces $\C P^{4}$ are isomorphic if and only if they have the same Chern classes. Moreover, the Chern classes of rank $3$ complex vector bundles over $\C P^{4}$ are determined. Combing Thomas's and Switzer's results with our work, we can assert that complex vector bundles over $\C P^{4}$ are all classified.
