On triviality of the mod p Hopf invariant
On triviality of the mod p Hopf invariant
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论 mod p Hopf 不变量的平凡性
DOI：
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发表时间：
1961
期刊：
影响因子：
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通讯作者：
Tsuneyo Yamanoshita
中科院分区：
文献类型：
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作者：
Nobuo Shimada;Tsuneyo Yamanoshita
导论.最近，J. F。亚当斯[2，3]给出了稳定的次上同调运算的公理化处理，并应用此公理化处理，证明了Hopf不变算子在n = 2n-1（Sn）（n·<$16）中不存在元素。由于这项工作，二次上同调运算成为代数拓扑学中的一个有用工具，沿着提供了令人满意的实用机器的主要运算，从而将有助于解决不少有趣的问题。本文遵循亚当斯给出的一般方案，将他关于mod 2 Hopf不变量的结果推广到mod p情形，其中p是奇素数.它将表明，模p霍普夫不变量
Introduction. Recently J. F. Adams [2, 3] gave an axiomatic treatment of stable secondary cohomology operations, and, applying this, proved the non-existence of elements of Hopf invariant one in ƒÎ2n-1(Sn)(n•†16). Owing to that work, the secondary cohomology operations turn out to be a useful tool in the algebraic topology, along with the primary operations, provided with satisfactory practical machinery, which will thus serve to solve not a few interesting problems. In the present paper, following the general scheme given by Adams, we shall extend his result on the mod 2 Hopf invariant to the mod p case, where p is an odd prime. It will be shown that the mod p Hopf invariant