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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An infinite family in $ \pi \sb\ast S\sp{0}$ derived from Mahowald's $ \eta \sb{j}$ family


Author: Robert R. Bruner
Journal: Proc. Amer. Math. Soc. 82 (1981), 637-639
MSC: Primary 55Q45; Secondary 55Q35
DOI: https://doi.org/10.1090/S0002-9939-1981-0614893-4
MathSciNet review: 614893
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Abstract: Combining the relationship due to D. S. Kahn between $ { \cup _i}$ operations in homotopy and Steenrod operations in the $ {E_2}$ term of the Adams spectral sequence with Mahowald's result that $ {h_1}{h_j}$ is a permanent cycle for $ j \geqslant 4$, we show that $ {h_2}h_j^2$ is also a permanent cycle for $ j \geqslant 5$. This gives another infinite family of nonzero elements in the stable homotopy of spheres. Properties of the $ { \cup _i}$ homotopy operations further imply that these elements generate $ {Z_2}$ direct summands.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0614893-4
Keywords: Stable homotopy of spheres, homotopy operation, Adams spectral sequence
Article copyright: © Copyright 1981 American Mathematical Society