FIXED SET SYSTEMS OF EQUIVARIANT INFINITE LOOP SPACES
FIXED SET SYSTEMS OF EQUIVARIANT INFINITE LOOP SPACES
复制标题
等变无限环空间的定集系统
DOI：
10.1090/s0002-9947-1991-1012523-4
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发表时间：
1991
影响因子：
1.3
通讯作者：
S. Waner
中科院分区：
文献类型：
--
作者：
S. Costenoble;S. Waner
我们开发的机器，使我们能够表明，适当的G-空间，包括BF的等变版本，等变无限循环空间。这涉及到一个“识别原理”的空间系统，表现为- mally像系统的固定集的G-空间;也就是说，我们给出了一个必要和充分条件，这样的系统是等价的固定集系统的等变无限循环空间。使用固定集系统语言的优点是，人们可以经常用等价的形式系统来代替实G-空间的固定集系统，该形式系统相当简单，并且允许去环所必需的几何。我们还应用这种机制来构造对应于Mackey函子的等变Eilenberg-Mac Lane空间。
We develop machinery enabling us to show that suitable G-spaces, including the equivariant version of BF , are equivariant infinite loop spaces. This involves a "recognition principle" for systems of spaces which behave for- mally like the system of fixed sets of a G-space; that is, we give a necessary and sufficient condition for such a system to be equivalent to the fixed set system of an equivariant infinite loop space. The advantage of using the language of fixed set systems is that one can frequently replace the system of fixed sets of an ac- tual G-space by an equivalent formal system which is considerably simpler, and which admits the requisite geometry necessary for delooping. We also apply this machinery to construct equivariant Eilenberg-Mac Lane spaces corresponding to Mackey functors.