p-局部紧群的正规化子分解
Normalizer decompositions of p-local compact groups
摘要：
本文给出了p-局部紧群（S，F，L）的一个正规化子分解，它把|L|描述为有限偏序集上的同伦余极限.我们的工作推广了Dwyer的有限群、Libman的p-局部有限群和Libman的紧李群的正规化子分解。我们的方法给出了一个结果，在李群的情况下，避免了拓扑微妙的奎伦定理A，因为我们的工作与离散群。我们计算了U（p）和SU（p）的p-完备分类空间以及Aguade和Zabrodsky的p-紧群的正规化子分解。
英文摘要：
We give a normalizer decomposition for a p-local compact group (S, F, L) that describes |L| as a homotopy colimit indexed over a finite poset. Our work generalizes the normalizer decompositions for finite groups due to Dwyer, for p-local finite groups due to Libman, and for compact Lie groups in separate work due to Libman. Our approach gives a result in the Lie group case that avoids topological subtleties with Quillen's Theorem A, because we work with discrete groups. We compute the normalizer decomposition for the p-completed classifying spaces of U(p) and SU(p) and for the p-compact groups of Aguade and Zabrodsky.
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