Skip to main content
SpringerLink
Log in

Applications and generalizations of the approximation theorem

  • Homotopy Theory
  • Conference paper
  • First Online:
Algebraic Topology Aarhus 1978

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 763))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. J. F. Adams. The Kahn-Priddy theorem. Proc. Camb. Phil. Soc. 73(1973), 45–55.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. G. Barratt. A free group functor for stable homotopy. Proc. Symp. Pure Math Vol.22, pp.31–35. Amer.Math.Soc. 1971.

    Google Scholar 

  3. M. G. Barratt and P. J. Eccles. Γ+ structures III. The stable structure of Ω∞Σ∞A. Topology 13(1974), 199–207.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Beck. On H-spaces and infinite loop spaces. Springer Lecture Notes in Mathematics Vol. 99, pp.139–153. 1969.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. M. Boardman and R. M. Vogt. Homotopy invariant algebraic structures on topological spaces. Springer Lecture Notes in Mathematics Vol 347. 1973.

    Google Scholar 

  6. E. H. Brown, Jr. and S. Gitler. A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra. Topology 12(1973), 283–295.

    Article  MathSciNet  MATH  Google Scholar 

  7. E. H. Brown, Jr. and F. P. Peterson. On the stable decomposition of Ω2Sn+r. Trans. Amer. Math. Soc. To appear.

    Google Scholar 

  8. E. H. Brown, Jr. and F. P. Peterson. The stable homotopy type of Ω2Sn+r. Quarterly J. Math. To appear.

    Google Scholar 

  9. J. Caruso. Thesis. Univ. of Chicago. In preparation.

    Google Scholar 

  10. J. Caruso, F. R. Cohen, J. P. May, and L. R. Taylor. James maps, Segal maps, and the Kahn-Priddy theorem. In preparation.

    Google Scholar 

  11. J. Caruso and S. Waner. An approximation to ΩnΣnX. To appear.

    Google Scholar 

  12. F. R. Cohen. Braid orientations and bundles with flat connections. Inventiones Math. 46(1978), 99–110.

    Article  MathSciNet  MATH  Google Scholar 

  13. F. R. Cohen, Little cubes and the classifying space for n-sphere fibrations. Proc. Symp. Pure Math. Vol.32 Part 2, pp.245–248. Amer. Math. Soc. 1978.

    Article  MATH  Google Scholar 

  14. F. R. Cohen, T. J. Lada, and J. P. May. The homology of iterated loop spaces. Springer Lecture Notes in Mathematics Vol 533. 1976.

    Google Scholar 

  15. F. R. Cohen, M. E. Mahowald, and R. J. Milgram. The stable decomposition for the double loop space of a sphere. Proc. Symp. Pure Math. Vol 32 Part 2, pp.225–228. Amer. Math. Soc. 1978.

    Article  MathSciNet  MATH  Google Scholar 

  16. F. R. Cohen, J. P. May, and L. R. Taylor. Splitting of certain spaces CX. Math. Proc. Camb. Phil. Soc. To appear.

    Google Scholar 

  17. F. R. Cohen, J. P. May, and L. R. Taylor. Splitting of some more spaces. Math. Proc. Camb. Phil. Soc. To appear.

    Google Scholar 

  18. F. R. Cohen, J. P. May, and L. R. Taylor. K(Z, 0) and K(Z2, 0) as Thom spectra. To appear.

    Google Scholar 

  19. F. R. Cohen, J. P. May, and L. R. Taylor. James maps and En ring spaces. In preparation.

    Google Scholar 

  20. F. R. Cohen and L. R. Taylor. Computations of Gelfand-Fuks cohomology, the cohomology of function spaces, and the cohomology of configuration spaces. Springer Lecture Notes in Mathematics Vol. 657, pp. 106–143. 1978.

    Article  MathSciNet  MATH  Google Scholar 

  21. R. L. Cohen. On odd primary stable homotopy theory. Thesis. Brandeis. 1978.

    Google Scholar 

  22. R. L. Cohen. The geometry of Ω2S3 and braid orientations. In preparation.

    Google Scholar 

  23. D. Davis. The antiautomorphism of the Steenrod algebra. Proc. Amer. Math. Soc. 44(1974), 235–236.

    Article  MathSciNet  MATH  Google Scholar 

  24. A. Dold and R. Thom. Quasifaserungen und unendliche symmetrische Produkte. Annals of Math. 67(1958), 239–281.

    Article  MathSciNet  MATH  Google Scholar 

  25. E. Dyer and R. K. Lashof. Homology of iterated loop spaces. Amer. J. Math. 84(1962), 35–88.

    Article  MathSciNet  MATH  Google Scholar 

  26. I. M. James. Reduced product spaces. Annals of Math. 62(1955), 170–197.

    Article  MathSciNet  MATH  Google Scholar 

  27. D. S. Kahn. On the stable decomposition of Ω∞S∞A. Springer Lecture Notes in Mathematics Vol 658, pp. 206–214. 1978.

    Article  MathSciNet  Google Scholar 

  28. D. S. Kahn and S. B. Priddy. The transfer and stable homotopy theory. Math. Proc. Camb. Phil. Soc. 83(1978), 103–111.

    Article  MathSciNet  MATH  Google Scholar 

  29. P. O. Kirley. On the indecomposability of iterated loop spaces. Thesis. Northwestern. 1975.

    Google Scholar 

  30. U. Koschorke and B. Sanderson. Self intersections and higher Hopf invariants. Topology 17(1978), 283–290.

    Article  MathSciNet  MATH  Google Scholar 

  31. G. Lewis. The stable category and generalized Thom spectra. Thesis. Chicago. 1978.

    Google Scholar 

  32. A. Liulevicius. The factorization of cyclic reduced powers by secondary cohomology operations. Memoirs Amer. Math. Soc. 42. 1962.

    Google Scholar 

  33. M. Mahowald. A new infinite family in 2π s* . Topology 16(1977), 249–256.

    Article  MathSciNet  MATH  Google Scholar 

  34. M. Mahowald and A. Unell. Bott periodicity at the prime 2 and the unstable homotopy of spheres. Preprint.

    Google Scholar 

  35. M. Mahowald. Some homotopy classes generated by ηj. These proceedings.

    Google Scholar 

  36. J. P. May. The geometry of iterated loop spaces. Springer Lecture Notes in Mathematics Vol 271. 1972.

    Google Scholar 

  37. J. P. May (with contributions by F. Quinn, N. Ray, and J. Tornehave). E∞ ring spaces and E69-4 ring spectra. Springer Lecture Notes in Mathematics Vol 577. 1977.

    Google Scholar 

  38. J. P. May. Infinite loop space theory. Bull. Amer. Math. Soc. 83(1977), 456–494.

    Article  MathSciNet  MATH  Google Scholar 

  39. J. P. May. Infinite loop space theory revisited. Proc. conf. alg. top. Waterloo, 1978.

    Google Scholar 

  40. D. McDuff. Configuration spaces of positive and negative particles. Topology 14(1975), 91–107.

    Article  MathSciNet  MATH  Google Scholar 

  41. R. J. Milgram. Iterated loop spaces. Annals of Math. 84(1966), 386–403.

    Article  MathSciNet  MATH  Google Scholar 

  42. J. W. Milnor. On the construction FK. In J. F. Adams. Algebraic Topology, a student's guide. London Math. Soc. Lecture Note Series 4, pp. 119–136. 1972.

    Google Scholar 

  43. G. Saitati. Loop spaces and K-theory. J. London Math. Soc. 9(1975), 423–428.

    Article  MathSciNet  Google Scholar 

  44. B. Sanderson. The geometry of Mahowald orientations. These proceedings.

    Google Scholar 

  45. G. B. Segal. Configuration-spaces and iterated loop spaces. Invent. Math. 21(1973), 213–222.

    Article  MathSciNet  MATH  Google Scholar 

  46. G. B. Segal. Operations in stable homotopy theory. London Math. Soc. Lecture Note Series 11, pp. 105–110. 1974.

    Google Scholar 

  47. V. P. Snaith. A stable decomposition of ΩnSnX. J. London Math. Soc. 7(1974), 577–583.

    Article  MathSciNet  MATH  Google Scholar 

  48. V. P. Snaith. On K*(Ω2X;Z2). Quarterly J. Math. 26(1975), 421–436.

    Article  MathSciNet  Google Scholar 

  49. N. E. Steenrod. Cohomology operations and obstructions to extending continuous functions. Advances in Math. 8(1972), 371–416.

    Article  MathSciNet  MATH  Google Scholar 

  50. H. Toda. Order of the identity class of a suspension space. Annals of Math. 78(1963), 300–323.

    Article  MathSciNet  MATH  Google Scholar 

  51. R. J. Wellington. The A-algebra H*Ω n+10 Σn+1X, the Dyer-Lashof algebra, and the Λ-algebra. Thesis. Chicago, 1977.

    Google Scholar 

  52. S. W. Yang. Thesis. Brandeis. 1978.

    Google Scholar 

Download references

Authors
  1. J. P. May
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Johan Louis Dupont Ib Henning Madsen

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer-Verlag

About this paper

Cite this paper

May, J.P. (1979). Applications and generalizations of the approximation theorem. In: Dupont, J.L., Madsen, I.H. (eds) Algebraic Topology Aarhus 1978. Lecture Notes in Mathematics, vol 763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088077

Download citation

  • DOI: https://doi.org/10.1007/BFb0088077

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09721-1

  • Online ISBN: 978-3-540-38520-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation