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On the differentials in the Adams spectral sequence for the stable homotopy groups of spheres. II

Published online by Cambridge University Press:  24 October 2008

C. R. F. Maunder
C. R. F. Maunder
Affiliation:
Christ's College, Cambridge
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Extract

In (7), we investigated some elements in the Adams spectral sequence for the stable homotopy groups of spheres, and proved that they were never boundaries, for any differential. This paper extends and generalizes these results: we consider more elements than in (7), and also prove that many of them do not survive to the E∞ term, so that they fail to be cycles for some dr, and this differential is therefore non-zero.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 4 , October 1965 , pp. 855 - 868
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

(1) Adams, J. F. On the non-existence of elements of Hopf invariant one. Ann. of Math. 72 (1960), 20–104.Google Scholar
(2) Adams, J. F. Stable homotopy theory (Mimeographed notes; Berkeley, 1961).Google Scholar
(3) Adams, J. F. On Chern characters and the structure of the unitary group. Proc. Cambridge Philos. Soc. 57 (1961), 189–199.CrossRefGoogle Scholar
(4) Adams, J. F. Lectures on K*(X). (Mimeographed notes; Manchester, 1963).Google Scholar
(5) Adams, J. F. On the groups J(X). IV. Topology (to appear).Google Scholar
(6) Maunder, C. R. F. Chern characters and higher order cohomology operations. Proc. Cambridge Philos. Soc. 60 (1964), 751–764.Google Scholar
(7) Maunder, C. R. F. On the differentials in the Adams spectral sequence for the stable homotopy groups of spheres. I. Proc. Cambridge Philos. Soc. 61 (1965), 53–60.Google Scholar
(8) Stong, R. Determination of H*(BO(k, …, ∞), Z 2) and H*(BU(k, …, ∞), Z 2). Trans. American Math. Soc. 107 (1963), 526–544.Google Scholar
(9) Thom, R. Espaces fibrés en sphères et Carrés de Steenrod. Ann. Sci. École. Norm. Sup. (3) 69 (1952), 109–182.CrossRefGoogle Scholar
(10) Thom, R. Quelques propriétés globales des variétés differentiables. Comm. Math. Helv. 28 (1954), 17–86.Google Scholar
(11) Toda, H. On exact sequences in the Steenrod algebra mod 2. Mem. Coll. Sci. Univ. Kyoto Ser. A 31 (1958), 33–64.Google Scholar