A Segal conjecture for p-completed classifying spaces
A Segal conjecture for p-completed classifying spaces
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p-完备分类空间的 Segal 猜想
DOI：
10.1016/j.aim.2007.04.006
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发表时间：
2005
影响因子：
1.7
通讯作者：
Kári Ragnarsson
中科院分区：
文献类型：
--
作者：
Kári Ragnarsson
我们提出并证明了Segal猜想的一个新的变形，它描述了从有限群G的p-完备分类空间到紧李群K的分类空间的稳定映射的同伦类群作为有限主（G，K）-丛的Grothendieck群Ap（G，K）的p-adic完备，其中主（G，K）-丛的各向同性群是p-群.综合不同素数p的结果，得到了群的（不完全）分类空间之间稳定映射的同伦类群的一个新的简单刻画。这个描述允许我们确定从有限主（G，K）-丛的Grothendieck群A（G，K）到BG到BK的稳定映射的同伦类群的映射的核。
We formulate and prove a new variant of the Segal conjecture describing the group of homotopy classes of stable maps from the p-completed classifying space of a finite group G to the classifying space of a compact Lie group K as the p-adic completion of the Grothendieck group Ap(G,K) of finite principal (G,K)-bundles whose isotropy groups are p-groups. Collecting the result for different primes p, we get a new and simple description of the group of homotopy classes of stable maps between (uncompleted) classifying spaces of groups. This description allows us to determine the kernel of the map from the Grothendieck group A(G,K) of finite principal (G,K)-bundles to the group of homotopy classes of stable maps from BG to BK.