Higher K-Theories pp 244-255 | Cite as

Transfer, symmetric groups, and stable homotopy theory

• Authors
• Authors and affiliations

• Stewart B. Priddy

Toward Some Calculations

First Online: 27 August 2006

• 2 Citations
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Part of the Lecture Notes in Mathematics book series (LNM, volume 341)

Keywords

Symmetric Group Homotopy Group Loop Space Cohomology Theory Symmetric Product 

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

1. [A]
   J. F. Adams, The Kahn-Priddy theorem, (to appear).Google Scholar
2. [AK]
   S. Araki and T. Kudo, Topology of H_n-spaces and H-squaring operations, Mem. Fac. Sci. Kyūsyū Univ. Ser. A. 10 (1956), 85–120.MathSciNetzbMATHGoogle Scholar
3. [BKP]
   M. Barratt, D. Kahn and S. Priddy, On Ω^∞S^∞ and the infinite symmetric group, Proc. of Sympos. Pure Math., vol. 22, Amer. Math. Soc., Providence, R.I., (1971).Google Scholar
4. [BP]
   M. Barratt, S. Priddy, On the homology of non-connected monoids and their associated groups, Comment. Math. Helv. 47 (1972), 1–14.MathSciNetCrossRefzbMATHGoogle Scholar
5. [B]
   J. Boardman and R. Vogt, Homotopy-everything H-spaces, Bull. Amer. Math. Soc., 74 (1968), 1117–1122.MathSciNetCrossRefzbMATHGoogle Scholar
6. [Br]
   W. Browder, Homology operations and loop spaces, Ill. J. Math., 4 (1960), 347–357.MathSciNetzbMATHGoogle Scholar
7. [D]
   A. Dold, Decomposition theorems for S(n)-complexes, Annals of Math., 75 (1962), 8–16.MathSciNetCrossRefzbMATHGoogle Scholar
8. [DL]
   E. Dyer and R. Lashof, Homology of iterated loop spaces, Amer. J. of Math., 84 (1962), 35–88.MathSciNetCrossRefzbMATHGoogle Scholar
9. [KP1]
   D. Kahn and S. Priddy, Applications of the transfer to stable homotopy theory (to appear Bull. A.M.S. 1972).Google Scholar
10. [KP2]
    D. Kahn and S. Priddy, The transfer and stable homotopy theory (in preparation).Google Scholar
11. [KP3]
    D. Kahn and S. Priddy, On the transfer in the homology of symmetric groups (in preparation).Google Scholar
12. [Mh]
    M. Mahowald, The metastable homotopy of Sⁿ, Amer. Math. Soc. Memoir No. 72 (1967).Google Scholar
13. [M1]
    J. P. May, The geometry of iterated loop spaces, Lecture Notes in Math., vol. 271, Springer-Verlag, 1972.Google Scholar
14. [M2]
    J. P. May, The homology of E_∞ spaces and infinite loop spaces, (in preparation).Google Scholar
15. [N1]
    M. Nakaoka, Cohomology theory of a complex with a transformation of prime period and its applications, J. of Inst. of Polytechnics, Osaka City Univ., 7 (1956), 51–102.MathSciNetzbMATHGoogle Scholar
16. [N2]
    M. Nakaoka, Cohomology mod p of symmetric products of sphere II, J. of Inst. Polytechnics, 10 (1959), 67–89.MathSciNetzbMATHGoogle Scholar
17. [N3]
    M. Nakaoka, Decomposition theorem for homology groups of symmetric groups, Annals of Math., 71 (1960), 16–42.MathSciNetCrossRefzbMATHGoogle Scholar
18. [N4]
    M. Nakaoka, Homology of the infinite symmetric group, Annals of Math., 73 (1961), 229–257.MathSciNetCrossRefzbMATHGoogle Scholar
19. [P]
    S. Priddy, Fredholm permutations and Ω^∞-1S^∞, (to appear).Google Scholar
20. [Q]
    D. Quillen, Higher K-theory. Proceedings of the Conference on Algebraic K-Theory, (1972).Google Scholar
21. [S1]
    G. Segal, The J-homomorphism. Proceedings of the Conference on Algebraic K-theory, (1972).Google Scholar
22. [S2]
    G. Segal, Categories and cohomology theories, (to appear).Google Scholar
23. [St]
    N. Steenrod, Cohomology operations, and obstructions to extending continuous functions, Advances in Math., 8 (1972), 371–416.MathSciNetCrossRefzbMATHGoogle Scholar
24. [W]
    J. Wagoner, Delooping classifying spaces in algebraic K-theory, (to appear).Google Scholar
25. [Wh]
    G. Whitehead, Recent Advances in Homotopy Theory, Regional Conference Series in Mathematics, No. 5 (1970).Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

• Stewart B. Priddy
  • 1

1. 1.Northwestern UniversityEvanstonU.S.A.