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Obstruction theory and K-theory

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

Keywords

  • Exact Sequence
  • Vector Bundle
  • Spectral Sequence
  • Homotopy Group
  • Obstruction Theory

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References

  1. J. F. Adams, "Vector fields on spheres," Ann. of Math. 75(1962) 603–632.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. M. F. Atiyah, "Thom complexes," Proc. London Math. Soc. 11(1961) 291–310.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. M. F. Atiyah, "Vector bundles and the Kunneth formula," Topology 1 (1962) 245–248.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. D. M. Davis, "Generalized homology and the generalized vector field problem," Quar. Jour. Math Oxford 25(1974) 169–193.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. D. M. Davis, "The cohomology of the spectrum bJ," Bol. Soc. Mat. Mex. 1976.

    Google Scholar 

  6. D. M. Davis, "The BP-coaction for projective spaces," to appear.

    Google Scholar 

  7. D. M. Davis and M. Mahowald, "The Geometric dimension of some vector bundles over projective spaces," Trans. Amer. Math. Soc. 205(1975) 295–315.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. D. M. Davis and M. Mahowald, "A strong nonimmersion theorem for RP81+7," Bull. Amer. Math. Soc. 81(1975) 155–156.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. D. M. Davis and M. Mahowald, "The immersion conjecture is false," to appear.

    Google Scholar 

  10. S. Gitler, K. Y. Lam, and M. Mahowald, to appear.

    Google Scholar 

  11. S. Gitler and M. Mahowald, "The geometric dimension of real stable vector bundles," Biol. Soc. Mat. Mex. 11(1966) 85–107.

    MathSciNet  MATH  Google Scholar 

  12. __________, Addendum, 12 (1967) 32–34.

    MathSciNet  Google Scholar 

  13. S. Gitler, M. Mahowald, and R. J. Milgram, "The nonimmersion problem for RPn and higher-order cohomology operations," Proc. Nat. Acad. Sci. U. S. A. 60(1968), 432–437.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. I. M. James, "On the immersion problem for real projective spaces," Bull. Amer. Math. Soc. 69(1963), 231–238.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. L. Kristensen, "On the cohomology of 2-stage Postnikov systems," Acta Math. 107(1962), 73–123.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. M. Mahowald, "The metastable homotopy of Sn," Memoirs Amer. Math. Soc. 72(1967).

    Google Scholar 

  17. M. Mahowald, "The order of the image of the J-homomorphism," Bull. Amer. Math. Soc. 76(1970), 1310–1313.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. M. Mahowald and R. J. Milgram, "Operations which detect Sq4 in connective K-theory and their applications, to appear.

    Google Scholar 

  19. M. Mahowald and R. Rigdon, "Obstruction theory with coefficients in a spectrum," Trans. Amer. Math. Soc. 204 (1975) 365–384.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. R. J. Milgram, "The Steenrod algebra and its dual for connective K-theory," Notas de Matematicas y Simposia, 1(1975) Soc. Mat. Mex. 127–158.

    MathSciNet  MATH  Google Scholar 

  21. B. Sanderson, "Immersions and embeddings of projective spaces," Proc. London Math. Soc. 53(1964), 137–153.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. G. W. Whitehead, "Generalized homology theories," Trans. Amer. Math. Soc. 102(1962), 227–283.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1978 Springer-Verlag

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Davis, D.M., Mahowald, M. (1978). Obstruction theory and K-theory. 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/BFb0068713

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  • DOI: https://doi.org/10.1007/BFb0068713

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08859-2

  • Online ISBN: 978-3-540-35808-4

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