p-局部有限群分类空间上的向量丛与Benson-Carlson对偶
Vector bundles over classifying spaces of p-local finite groups and Benson-Carlson duality
摘要：
本文给出了p-局部有限群的分类空间上复向量丛的Grothendieck群在其Sylow子群的表示环上的一个刻划。证明了p-局部有限群的广义上同调不变量的稳定元公式，并利用该公式证明了p-局部有限群的酉嵌入的存在性.最后，证明了p-局部有限群的分类空间的上链的增广映射是Dwyer-Greenlees-Iyengar意义下的Gorenstein，并得到了这类分类空间的上同调环的一些结果.
英文摘要：
In this paper we obtain a description of the Grothendieck group of complex vector bundles over the classifying space of a p-local finite group in terms of representation rings of subgroups of its Sylow. We also prove a stable elements formula for generalized cohomological invariants of p-local finite groups, which is used to show the existence of unitary embeddings of p-local finite groups. Finally, we show that the augmentation map for the cochains of the classifying space of a p-local finite group is Gorenstein in the sense of Dwyer-Greenlees-Iyengar and obtain some consequences about the cohomology ring of these classifying spaces.
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