Equivariant Stable Homotopy Theory
Equivariant Stable Homotopy Theory
复制标题
等变稳定同伦理论
DOI：
10.1007/bfb0075778
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发表时间：
1986
影响因子：
1.4
通讯作者：
M. Steinberger
中科院分区：
文献类型：
--
作者：
L. Lewis;Jon P. May;M. Steinberger
过去十年来，这一领域的活动非常活跃。本章简要介绍了空间级等变同伦理论的基本概念。介绍了谱级等变同伦理论的基本思想和结构。本章还通过解释有关等变、非等变同调和上同调的基本定位和补全定理来说明思想。为了保持轨道与齐次空间之间的同胚性，必须将注意力限制在闭子群上。紧李群有两大优点：子群结构相当简单（附近的子群是共轭的），并且有足够的表示(任何足够好的（7-空间嵌入在一个中）。
The last decade has seen a great deal of activity in this area. The chapter provides a brief sketch of the basic concepts of space-level equivariant homotopy theory. It also provides an introduction to the basic ideas and constructions of spectrum-level equivariant homotopy theory. The chapter also illustrates ideas by explaining the fundamental localization and completion theorems that relate equivariant to nonequivariant homology and cohomology. To retain the homeomorphism between orbits and homogeneous spaces one shall always restrict attention to closed subgroups. The class of compact Lie groups has two big advantages: the subgroup structure is reasonably simple (nearby subgroups are conjugate), and there are enough representations (any sufficiently nice (7-space embeds in one).