A new differential in the Adams spectral sequence
A new differential in the Adams spectral sequence
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DOI：
10.1016/0040-9383(84)90010-7
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发表时间：
1984
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影响因子：
--
通讯作者：
R. Bruner
中科院分区：
文献类型：
--
作者：
R. Bruner
1 美元。 Barratt 等人一系列论文的简介 [1,6,14,15]。使用 Adams 谱序列确定了 29 I n 5 45 的 rnSo 2 分量以及该范围内的许多产品和 Toda 括号。在本文中，我们证明存在一个额外的非零微分，并确定其对产品和 Toda 括号的影响。新的微分源自 Makinen [7] 将微分和球体 Adams 谱序列中的 Steenrod 运算相关联的一般公式。有趣的是，Milgram [l 1] 通过相同类型的更有限的公式在 [6] 中发现了类似的错误（在 [1] 中纠正）。我们给出 Makinen 的一般公式，单位为 2 美元。然后我们收集 sc 的 Adams 谱序列中的一些已知计算结果。所以3美元。我们的新结果以 4 美元的形式呈现，而 5 美元包含新的结果证明，其已发布的证明依赖于我们正在纠正的错误。
$1. INTRODUCTION IN A SERIES of papers [1, 6, 14, 15], Barratt et al. used the Adams spectral sequence to determine the 2 component of rnSo for 29 I n 5 45 together with a number of products and Toda brackets in this range. In this paper we show that there is an additional nonzero differential and determine its implications for products and Toda brackets. The new differential follows from a general formula due to Makinen [7] relating differentials and Steenrod operations in the Adams spectral sequence of a sphere. It is interesting to note that Milgram [l 1] found a similar mistake in [6](corrected in [1]) by means of a more limited formula of the same type. We give Makinen’s general formula in $2. We then collect some known calculations in the Adams spectral sequence for sc. SO in $3. Our new results are presented in $4, while $5 contains new proofs of results whose published proofs rely on the mistake we are correcting.