A note on the Kahn-Priddy map

Juno MUKAI

doi:10.2969/jmsj/04010053

Juno MUKAI

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JOURNAL FREE ACCESS

1988 Volume 40 Issue 1 Pages 53-63

DOI https://doi.org/10.2969/jmsj/04010053

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Published: 1988 Received: June 12, 1986 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Hirosi Toda on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. F. Adams, Vector fields on spheres, Ann. of Math., 75 (1962), 603-632.
2) J. F. Adams, On the groups J(X)-IV, Topology, 5 (1966), 21-71.
3) M. Fujii, K₀-groups of projective spaces, Osaka J. Math., 4 (1967), 141-149.
4) K. Iriye, On the James number of cyclic maps of spheres, Japan. J. Math., 10 (1984), 1-8.
5) I. M. James, The topology of Stiefel manifolds, London Math. Soc., Lecture Note, 24, Cambridge Univ., 1976.
6) I. M. James, E. Thomas, H. Toda and G. W. Whitehead, On the symmetric square of a sphere, J. Math. Mech., 12 (1963), 771-776.
7) D. S. Kahn and S. B. Priddy, Applications of the transfer to stable homotopy theory, Bull. Amer. Math. Soc., 78 (1972), 981-987.
8) T. Kambe, The structure of K^Λ-rings of the lens space and their applications, J. Math. Soc. Japan, 18 (1966), 135-146.
9) T. Kobayashi, Non-immersion theorems for lens spaces. II, J. Sci. Hiroshima Univ., Ser. A-I, 32 (1968), 285-292.
10) K. Y. Lam, KO-equivalences and existence of nonsingular bilinear maps, Pacific J. Math., 82 (1979), 145-154.
11) M. Mimura, J. Mukai and G. Nishida, Representing elements of stable homotopy groups by symmetric maps, Osaka J. Math., 11(1974), 105-111.
12) J. Mukai, A characterization of the Kahn-Priddy map, Advanced Studies in Pure Math., 9 (1986), 287-291.
13) J. Mukai, On the stable homotopy of the real projective space of even low dimension, Publ. RIMS, Kyoto Univ., 22 (1986), 81-95.
14) G. Nishida, The nilpotency of elements of the stable homotopy groups of spheres, J. Math. Soc. Japan, 25 (1973), 707-732.
15) G. Nishida, On the algebraic K-group of lens spaces and its applications, J. Math. Kyoto Univ., 23 (1983), 211-217.
16) H. Toda, Order of the identity class of a suspension space, Ann. of Math., 78 (1963), 300-325.
17) H. Toda, On iterated suspensions I, J. Math. Kyoto Univ., 5 (1965), 87-142.
18) H. Toda, On iterated suspensions II, J. Math. Kyoto Univ., 5 (1966), 209-250.
19) J. Ucci, On cyclic and iterated cyclic products of spheres, Osaka J. Math., 8 (1971), 393-404.

Right : [1] J. F. Adams, Vector fields on spheres, Ann. of Math., 75 (1962), 603-632.
[2] J. F. Adams, On the groups J(X)-IV, Topology, 5 (1966), 21-71.
[3] M. Fujii, K₀-groups of projective spaces, Osaka J. Math., 4 (1967), 141-149.
[4] K. Iriye, On the James number of cyclic maps of spheres, Japan. J. Math., 10 (1984), 1-8.
[5] I. M. James, The topology of Stiefel manifolds, London Math. Soc., Lecture Note, 24, Cambridge Univ., 1976.
[6] I. M. James, E. Thomas, H. Toda and G. W. Whitehead, On the symmetric square of a sphere, J. Math. Mech., 12 (1963), 771-776.
[7] D. S. Kahn and S. B. Priddy, Applications of the transfer to stable homotopy theory, Bull. Amer. Math. Soc., 78 (1972), 981-987.
[8] T. Kambe, The structure of K^Λ-rings of the lens space and their applications, J. Math. Soc. Japan, 18 (1966), 135-146.
[9] T. Kobayashi, Non-immersion theorems for lens spaces. II, J. Sci. Hiroshima Univ., Ser. A-I, 32 (1968), 285-292.
[10] K. Y. Lam, KO-equivalences and existence of nonsingular bilinear maps, Pacific J. Math., 82 (1979), 145-154.
[11] M. Mimura, J. Mukai and G. Nishida, Representing elements of stable homotopy groups by symmetric maps, Osaka J. Math., 11 (1974), 105-111.
[12] J. Mukai, A characterization of the Kahn-Priddy map, Advanced Studies in Pure Math., 9 (1986), 287-291.
[13] J. Mukai, On the stable homotopy of the real projective space of even low dimension, Publ. RIMS, Kyoto Univ., 22 (1986), 81-95.
[14] G. Nishida, The nilpotency of elements of the stable homotopy groups of spheres, J. Math. Soc. Japan, 25 (1973), 707-732.
[15] G. Nishida, On the algebraic K-group of lens spaces and its applications, J. Math. Kyoto Univ., 23 (1983), 211-217.
[16] H. Toda, Order of the identity class of a suspension space, Ann. of Math., 78 (1963), 300-325.
[17] H. Toda, On iterated suspensions I, J. Math. Kyoto Univ., 5 (1965), 87-142.
[18] H. Toda, On iterated suspensions II, J. Math. Kyoto Univ., 5 (1966), 209-250.
[19] J. Ucci, On cyclic and iterated cyclic products of spheres, Osaka J. Math., 8 (1971), 393-404.

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