Skip to main content

Cohomology operations and vector fields

  • Conference paper
  • First Online:
Geometric Applications of Homotopy Theory II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 658))

  • 626 Accesses

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

Access this chapter

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.

References

  1. Adams, J.F. "Vector fields on spheres," Ann. Math., 75(1962).

    Google Scholar 

  2. Araki, S. and T. Kudo. "Topology of Hn-spaces and H-squaring operations," Mem. Fac. Sci. Kyūsyū Univ. Ser. A, 10(1956), 85–120.

    MathSciNet  MATH  Google Scholar 

  3. Barratt, M.G. "The quadratic construction" (unpublished), Conference on Algebraic Topology at the University of Illinois, Chicago Circle, 1968.

    Google Scholar 

  4. Browder, W. "Homology operations and loop spaces," Ill. J. of Math., 4(1961), 347–357.

    MathSciNet  MATH  Google Scholar 

  5. Dyer, E. and R. Lashoff. "Homology of iterated loop spaces," Amer. J. of Math., 84(1962), 35–88.

    Article  MathSciNet  MATH  Google Scholar 

  6. Frank, D. and E. Thomas. "A generalization of the Steenrod-Whitehead vector field theorem," Top. 7(1968), 311–316.

    MathSciNet  MATH  Google Scholar 

  7. Hopf, H. "Vectorfelder in n-dimensionaler Mannigfaltigkeiten," Math. Annln. 96(1927), 225–250.

    Article  MathSciNet  Google Scholar 

  8. Hu, S.T. Homotopy Theory, Academic Press, New York (1959).

    MATH  Google Scholar 

  9. Hurwitz, A. "Über die Komposition der quadratischen Formen," Math. Ann. Biol., 88(1923), 1–25. (Math. Werke II, 641–666; Seiten angaben in unserem Text beziehen sich auf den Abdruck in den Math. Werken.)

    Article  MathSciNet  Google Scholar 

  10. Kahn, D.S. "Cup-i products and the Adams spectral sequence," Top. 9(1970), 1–9.

    MathSciNet  MATH  Google Scholar 

  11. Mahowald, M.E. "On the metastable homotopy of Sn," Mem. Amer. Math. Soc. No. 72 (1967).

    Google Scholar 

  12. Michelsohn, M.L. "Decompositions of Steenrod Squares," preprint (1976), University of California, Berkeley.

    Google Scholar 

  13. _____. "Vector fields on manifolds," preprint (1977), University of California, Berkeley.

    Google Scholar 

  14. Milgram, R.J. "Unstable homotopy from the stable point of view," Lecture Notes in Mathematics, No. 368, Springer-Verlag (1974).

    Google Scholar 

  15. Poincaré, H. "Analysis Situs," Paris J. Ecole Polytechn., ser. 2, 1(1895), 1–121.

    MATH  Google Scholar 

  16. Radon, J. "Lineare Scharen orthogonaler Matrizen," Abh. Sem. Hamburg I (1923), 1–14.

    MathSciNet  MATH  Google Scholar 

  17. Steenrod, N.E. and J.H.C. Whitehead. "Vector fields on the n-sphere," Proc. Nat'l. Acad. Sci. U.S.A., 37(1951), 58–63.

    Article  MathSciNet  MATH  Google Scholar 

  18. Toda, H. "Vector fields on spheres," Bull. Amer. Math. Soc. 67(1961), 408–412.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

M. G. Barratt M. E. Mahowald

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer-Verlag

About this paper

Cite this paper

Michelsohn, M.L. (1978). Cohomology operations and vector fields. In: Barratt, M.G., Mahowald, M.E. (eds) Geometric Applications of Homotopy Theory II. Lecture Notes in Mathematics, vol 658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068723

Download citation

  • DOI: https://doi.org/10.1007/BFb0068723

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08859-2

  • Online ISBN: 978-3-540-35808-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics