An infinite family in $\pi _\ast S^{0}$ derived from Mahowald’s $\eta _{j}$ family
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- by Robert R. Bruner PDF
- Proc. Amer. Math. Soc. 82 (1981), 637-639 Request permission
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.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- 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