Hiroshima Mathematical Journal

The stable homotopy groups of spheres. III

Shichirô Oka

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 5, Number 3 (1975), 407-438.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206136536

Digital Object Identifier
doi:10.32917/hmj/1206136536

Mathematical Reviews number (MathSciNet)
MR0394651

Zentralblatt MATH identifier
0308.55013

Subjects
Primary: 55E40

Citation

Oka, Shichirô. The stable homotopy groups of spheres. III. Hiroshima Math. J. 5 (1975), no. 3, 407--438. doi:10.32917/hmj/1206136536. https://projecteuclid.org/euclid.hmj/1206136536


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References

  • [1] J. F. Adams, On the groups J (X)-IV, Topology 5 (1966), 21-71.
  • [2] H. H. Gershenson, Relationships between the Adams spectral sequence and Toda's calculations of the stable homotopy groups of spheres, Math. Zeit. 81 (1963), 223-259.
  • [3] A. Liulevicius, The factorization of cyclic reduced powers by secondary cohomology operations, Mem. Amer. Math. Soc. 42, Providence, 1962.
  • [4] J. P. May, The cohomology of restricted Lie algebras and of Hopf algebras', application to the Steenrod algebra, Dissertation, Princeton University, Princeton, 1964.
  • [5] O. Nakamura, On the cohomology of the mod Steenrod algebra, y Bull. Sci. Engrg. Div. Univ. Ryukyus (Math. Nat. Sci.) 18 (1975), 9-58, Naha, Okinawa.
  • [6] O. Nakamura, Some differentials in the mod 3 Adams spectral sequence, Bull. Sci. Engrg. Div. Univ. Ryukyus (Math. Nat. Sci.) 19 (1975), 1-26, Naha, Okinawa.
  • [7] S. Oka, Some exact sequences of modules over the Steenrod algebra, Hiroshima Math. J. 1 (1971), 109-121.
  • [8] S. Oka, The stable homotopy groups of spheres I, II, Hiroshima Math. J. 1 (1971), 305-337; 2 (1972), 99-161.
  • [9] S. Oka, On the stable homotopy ring of Moore spaces, Hiroshima Math. J. 4 (1974), 629-678.
  • [10] S. Oka, H. Toda, Non-triviality of an element in the stable homotopy groups of spheres, Hiroshima Math. J. 5 (1975), 115-125,
  • [11] N. Shimada and T. Yamanoshita, On triviality of the mop Hop/ invariant, Jap. J. Math. 31 (1961), 1-24.
  • [12] L. Smith, On realizing complex bordism modules. Applications to the homotopy of spheres, Amer. J. Math. 92 (1970), 793-856.
  • [13] P. E. Thomas and R. Zahler, Generalized higher order cohomology operations and stable homotopygroups of spheres, to appear in Adv. Math.
  • [14] H. Toda, p-Primary components of homotopygroups, I. Exact sequences in Steenrod algebra; II. modp Hopf invariant', III. Stable groups of the sphere', IV. Compositions and tone constructions, Mem. Coll. Sci. Univ. Kyoto, Ser. A, 31 (1958), 129-142; 143-160; 191- 210; 32 (1959), 288-332.
  • [15] H. Toda, On iterated suspensions, J. Math. Kyoto Univ. 5 (1965), 87-142; 209-250; 8 (1968), 101-130.
  • [16] H. Toda, An important relation in homotopy groups of spheres, Proc. Japan Acad. 43 (1967), 839-842.
  • [17] H. Toda, Extended p-th powers of complexes and applications to homotopy theory, Proc. Japan Acad. 44 (1968), 198-203.
  • [18] H. Toda, Algebra of stable homotopyof Zp -spaces and applications, J. Math. Kyoto Univ.11 (1971), 197-251.
  • [19] R. Zahler, Existence of the stable homotopy family t, Bull. Amer. Math. Soc. 79 (1973), 787-789.

See also

  • Part I: Shichirô Oka. The stable homotopy groups of spheres. I. Hiroshima Math. J., Volume 1, Number 2, (1971), 305--337.
  • Part II: Shichirô Oka. A new family in the stable homotopy groups of spheres. II. Hiroshima Math. J., Volume 6, Number 2, (1976), 331--342.
  • Part II: Shichirô Oka. The stable homotopy groups of spheres. II. Hiroshima Math. J., Volume 2, Number 1, (1972), 99--161.