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On the differentials in the Adams spectral sequence

Published online by Cambridge University Press:  24 October 2008

C. R. F. Maunder
C. R. F. Maunder
Affiliation:
University of Southampton
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Extract

In this paper, we shall prove a result which identifies the differentials in the Adams spectral sequence (see (1,2)) with certain cohomology operations of higher kinds, in the sense of (4). This theorem will be stated precisely at the end of section 2, after a summary of the necessary information about the Adams spectral sequence and higher-order cohomology operations; the proof will follow in section 3. Finally, in section 4, we shall consider, by way of example, the Adams spectral sequence for the stable homotopy groups of spheres: we show how our theorem gives a proof of Liulevicius's result that , where the elements hn (n ≥ 0) are base elements of

corresponding to the elements Sq2n in A, the mod 2 Steenrod algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 3 , July 1964 , pp. 409 - 420
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1) Adams, J. F. On the structure and applications of the Steenrod algebra. Comment. Math. Helv. 32 (1958), 180–214.CrossRefGoogle Scholar
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(3) Adams, J. F. On the non-existence of elements of Hopf invariant one. Ann. of Math. 72 (1960), 20–104.CrossRefGoogle Scholar
(4) Maunder, C. R. F. Cohomology operations of the Nth. kind. Proc. London Math. Soc. (3) 13 (1963), 125–154.CrossRefGoogle Scholar