Minimal atlases of real projective spaces

  • Michael J. Hopkins
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1370)


Vector Bundle Projective Space Tangent Bundle Normal Bundle Smash 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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  1. 1.
    J. F. Adams: On Chern characters and the structure of the unitary group, Proc. Cam. Phil. Soc. 57 (1961), 189–199.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    J. F. Adams: Stable homotopy and generalized cohomology, University of Chicago Press 1974.Google Scholar
  3. 3.
    J. F. Adams and H. R. Margolis: Modules over the Steenrod algebra, Topology, 10(1971), 271–282.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    J. F. Adams and S. B. Priddy: Uniqueness of BSO, Proc. Cam. Phil. Soc. 80 (1976), 475–509.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    J. Adem, S. Gitler and I. M. James: On axial maps of a certain type, Bol. Soc. Mat. Mex. 17 (1972), 59–62.Google Scholar
  6. 6.
    I. Berstein: On imbedding numbers of differentiable manifolds, Topology 7 (1968), 95–109.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    I. Berstein and T. Ganea: The category of a map and of a cohomology class, Fundam. Math. (1962), 265–279.Google Scholar
  8. 8.
    R. H. Fox: On the Lusternik-Schnirelman Category, Ann. Math. 42 (1941), 333–370.CrossRefzbMATHGoogle Scholar
  9. 9.
    T. Ganea: A generalization of the homology and homotopy suspension, Comm. Math. Helv. 39 (1965), 295–322.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    T. Ganea: On the homotopy suspension, Comm. Math. Helv. 43(1968), 225–234.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    A. Haefliger and M. W. Hirsch: Immersions in the stable range, Ann. Math. 75 (1962), 231–241.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    M. W. Hirsch: Immersions of manifolds, Trans. Am. Math. Soc. 93 (1959), 242–276.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    M. W. Hirsch: Smooth regular neighbourhoods, Ann. Mth. 79 (1962), 524–530.CrossRefzbMATHGoogle Scholar
  14. 14.
    I. M. James: The space of bundle maps, Topology 2 (1963), 45–59.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    I. M. James: On category in the sense of Lusternik-Schnirelmann, Topology 17 (1978), 331–348.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    I. M. James: On category and section category, Proceedings of the 1979 Topology Conference, Brazilian Math. Soc., APUCI, Rio de Janera.Google Scholar
  17. 17.
    M. Mahowald: bo resolutions, Pac. J. of Math. 92 (1981), 365–383.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    R. J. Milgram: The Steenrod algebra and its dual for connective K-theory, Reunion Sobre Theorie de Homotopic Universidad de Northwestern 1974, Sociedad Matimatica Mexicana, 127–159.Google Scholar
  19. 19.
    F. P. Peterson: lectures on cobordism theory, Kinokuniya Book Store Co., Ltd. Tokyo, Japan, 1968.zbMATHGoogle Scholar
  20. 20.
    V. Poenaru: Sur la theorie des immersions, Topology 1 (1962), 81–100.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    R. E. Stong: Determination of H* (BO(k, ..., ∞); ℤ12) and H*(BU(k, ..., ∞); ℤ/2), Trans. Am. Math. Soc., 107 (1963), 526–544.MathSciNetzbMATHGoogle Scholar
  22. 22.
    A. S. Svarc: The genus of a fibre space, Am. Math. Soc. Transl. 55 (1966), 49–140.CrossRefGoogle Scholar
  23. 23.
    G. W. Whitehead: The homology suspension, Colloque de topologie algebrique, Louvain (1956), 89–95.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Michael J. Hopkins
    • 1
  1. 1.University of ChicagoUSA

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