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Vector bundles over classifying spaces of p‐local finite groups and Benson–Carlson duality
Journal of the London Mathematical Society ( IF 1.0 ) Pub Date : 2019-07-23 , DOI: 10.1112/jlms.12255
José Cantarero 1 , Natàlia Castellana 2 , Lola Morales 3
Affiliation  

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 ( S , F , L ) in terms of representation rings of subgroups of S . 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 C ( | L | p ; F p ) F p is Gorenstein in the sense of Dwyer–Greenlees–Iyengar and obtain some consequences about the cohomology ring of | L | p .

中文翻译:

p局部有限群和Benson-Carlson对偶性的分类空间上的向量束

在本文中,我们获得了在向量的分类空间上的复矢量束的Grothendieck群的描述。 p -局部有限群 小号 F 大号 就子群的表示环而言 小号 。我们还证明了广义同调不变量的稳定元素公式 p -局部有限群,用于显示存在一元嵌入 p -局部有限群。最后,我们证明了增强 C | 大号 | p ; F p F p 是Dwyer–Greenlees–Iyengar的Gorenstein,并且对 | 大号 | p
更新日期:2019-07-23
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