Another systematic phenomenon in the cohomology of the Steenrod algebra
Another systematic phenomenon in the cohomology of the Steenrod algebra
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Steenrod 代数上同调中的另一个系统现象
DOI：
10.1016/0040-9383(71)90015-2
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发表时间：
1971
期刊：
影响因子：
--
通讯作者：
M. Tangora
中科院分区：
文献类型：
--
作者：
H. Margolis;S. Priddy;M. Tangora
本文的目的是双重的。首先，我们描述了模2 Steenrod代数上同调中的一个新算子：H**（A）。该运算符将干度t-s增加4.5，过滤度s增加6。我们的主要结果是H**（A）的“楔形”子代数[4]在它之下每4.5个茎重复一次。第二，我们认为我们所使用的方法是通过研究H**（B）来研究H**（A）的有效性的进一步证据，其中适当地选择了A的子代数B。亚当斯[1]在制定他的周期性算子时非常成功地使用了这种技术，最近Zachariou [7]也成功地使用了这种技术来获得楔形的一部分。利用本文所用的子代数以外的子代数，我们得到了H**（A）的其它元素的信息，如n，r，IV，G，R，和W，（全文的符号见[6]）。这些结果将出现在其他地方。
THE PURPOSE of this paper is twofold. First, we describe a new operator in the cohomology of the mod 2 Steenrod algebra: H**(A). This operator increases the stem degree t-s by 4.5 and the filtration degree s by 6. It may be thought of as a kind of periodicity, and our main result is that under it the “wedge” subalgebra [4] of H**(A) is repeated every 4.5 stems. Second, we regard the methods we use as further evidence of the efficacy of the technique of studying H**(A) by studying H**(B) for suitably chosen subalgebra B of A. This technique has been used very successfully by Adams [l] in formulating his periodicity operator and more recently by Zachariou [7] to obtain part of the wedge. Using other subalgebras than that of this paper we have obtained information about other elements of H**(A) such as n, r, IV, G,, R, and W,(for the notation throughout the paper see [6]). These results will appear elsewhere.