Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic -Theory
Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic -Theory
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DOI：
10.1090/conm/346
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发表时间：
2004-05
期刊：
影响因子：
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通讯作者：
P. Goerss;S. Priddy
中科院分区：
文献类型：
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作者：
P. Goerss;S. Priddy
该项目的动机来自于对有限群空间（或更普遍的紧李群空间）进行分类的 p 局部同伦理论的研究。空间的“p局部同伦理论”是指其p-完备性的同伦理论。事实证明，BG 的 p-局部同伦理论与群 G 的“p-局部结构”之间存在密切联系，我们指的是 G 的 Sylow p-子群中的融合（共轭关系）。这种联系向我们建议了某些空间的构造（“p-局部有限群”和“p-局部紧群”的分类空间），这些空间具有许多与有限和紧李群的 p-完备分类空间相同的性质。 Bousfield-Kan p-完成函子的函数将在第 1 节中给出。出于本介绍的目的，只需说这是一个从空间到空间的函子，它重点关注通过其 mod p 同源性可见的空间属性。
The motivation for this project comes from the study of the p-local homotopy theory of classifying spaces of finite groups, or more generally of compact Lie groups. By “plocal homotopy theory” of a space we mean the homotopy theory of its p-completion. It turns out that there is a close connection between the p-local homotopy theory of BG and the “p-local structure” of the group G, by which we mean the fusion (conjugacy relations) in a Sylow p-subgroup of G. This connection then suggested to us the construction of certain spaces (classifying spaces of “p-local finite groups” and “p-local compact groups”) which have many of the same properties as have p-completed classifying spaces of finite and compact Lie groups.A brief survey of the Bousfield-Kan p-completion functor will be given in Section 1. For the purpose of this introduction it suffices to say that this is a functor from spaces to spaces, which focuses on the properties of a space which are visible through its mod p homology.