A periodicity theorem in homological algebra
A periodicity theorem in homological algebra
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同调代数中的周期性定理
DOI：
10.1017/s0305004100039955
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发表时间：
1966
影响因子：
0.8
通讯作者：
J. F. Adams
中科院分区：
文献类型：
--
作者：
J. F. Adams
介绍。在（1 - 3,6）中证明了同调代数可以应用于稳定同伦理论。在这个应用中，我们处理A -模，其中A是模p Steenrod代数。用这种方法得到一个具体的几何结果通常涉及两种不同的工作。为了说明这一点，我们考虑（1,2）的谱序列：这里可以有效地计算E2项中的每组Extss， t；这个过程是纯代数的。然而，对于计算谱序列中的微分dr，或者确定由E∞项建立的群扩展，没有给出这样的有效方法；这些都是拓扑问题。
Introduction. In (1–3,6) it is shown that homological algebra can be applied to stable homotopy-theory. In this application, we deal with A -modules, where A is the mod p Steenrod algebra. To obtain a concrete geometrical result by this method usually involves work of two distinct sorts. To illustrate this, we consider the spectral sequence of (1,2): Here each group Extss, t which occurs in the E2 term can be effectively computed; the process is purely algebraic. However, no such effective method is given for computing the differentials dr in the spectral sequence, or for determining the group extensions by which is built up from the E∞ term; these are topological problems.