标题： 关于某些李群和规范群的分类空间的Thom同态的一个注记 显示英文标题

标题： A note on the Thom morphism for the classifying space of certain Lie groups and gauge groups

摘要： 我们给出了除了 E_8 之外，例外李群类空间中哪些非挠生成元不在复配边到整上同调的 Thom 态射的像中。 然后我们证明了对于四维球面上主 E_7-丛的规范群的类空间，Thom 态射不是满射。 我们利用这些结果来检测李群及其类空间中约化 Thom 态射核中的非平凡元素。 显示英文摘要

摘要： We give a complete description of which non-torsion generators are not in the image of the Thom morphism from complex cobordism to integral cohomology for the classifying space of exceptional Lie groups except for E_8. We then show that the Thom morphism is not surjective for the classifying space of the gauge group of a principal E_7-bundle over the four-dimensional sphere. We use the results to detect nontrivial elements in the kernel of the reduced Thom morphism for Lie groups and their classifying spaces.