Generalized homology theories
Generalized homology theories
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DOI：
10.1090/s0002-9947-1962-0137117-6
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发表时间：
1962-02
影响因子：
1.3
通讯作者：
G. Whitehead
中科院分区：
文献类型：
--
作者：
G. Whitehead
1. 简介。众所周知，系数在阿贝尔群 II 中的多面体 X 的上同调群 Hn (X; II) 可以表征为 X 到 Eilenberg-MacLane 空间 K (ll, n) 的映射的同伦类群。此外，系数为II的上同调理论可以这样描述；一对上同调序列的共界同态的存在是由于对于每个 n 存在悬浮 SK (1l, n) 到 K (ll, n+ 1) 的自然映射；换句话说，空间K(ll，n)是谱(2)的分量。事实上，如果 E={En} 是一个谱，那么群
1. Introduction. It is well known that the cohomology groups Hn (X; II) of a polyhedron X with coefficients in the abelian group II can be characterized as the group of homotopy classes of maps of X into the Eilenberg-MacLane space K (ll, n). Moreover, the cohomology theory with coefficients in II can be described in this way; the existence of the coboundary homomorphism of the cohomology sequence of a pair is due to the fact that there are natural maps of the suspension SK (1l, n) into K (ll, n+ 1) for every n; in other words, the spaces K (ll, n) are the components of a spectrum (2). In fact, if E={En} is a spectrum, then the groups