Advertisement

Lectures on characteristic classes and foliations

  • Raoul Bott
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 279)

Keywords

Vector Bundle Normal Bundle Homotopy Class Invariant Polynomial Continuous Functor 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, 1963, Interscience Publishers, New York.zbMATHGoogle Scholar

References

  1. 1.
    A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces, II, Am. J. Math., 81 (1959), pp. 315–382.MathSciNetCrossRefGoogle Scholar
  2. 2.
    D. Husemoller, Fibre Bundles, McGraw-Hill, New York, 1966.CrossRefzbMATHGoogle Scholar
  3. 3.
    J. Milnor, Lectures on Characteristic Classes, (Notes by J. Stasheff), Mimeographed notes, Princeton Univ.Google Scholar
  4. 4.
    Munkres, Elementary Differential Topology, Annals of Math. Studies, No. 54, Princeton Univ. Press, Princeton, N. J., 1963.CrossRefzbMATHGoogle Scholar

References

  1. 1.
    A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces, I, Am. J. Math., 80 (1958), pp. 458–538.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962.zbMATHGoogle Scholar
  3. 3.
    S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, N. J., 1964.zbMATHGoogle Scholar
  4. 4.
    A. Weil, Sur les théorèmes de de Rham, Comment. Math. Helv., 26 (1952), pp. 119–145.MathSciNetCrossRefzbMATHGoogle Scholar

References

  1. 1.
    S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, Interscience Publishers, New York, N. Y., 1963.zbMATHGoogle Scholar
  2. 2.
    J. Milnor, Morse Theory, Princeton University Press, Princeton, N. J., 1963.CrossRefzbMATHGoogle Scholar

References

  1. 1.
    S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, N. J., 1964.zbMATHGoogle Scholar

References

  1. 1.
    W. S. Massey, Some higher order cohomology operations, Symposium Internacional de Topología Algebraica, Univ. Nac. Autonoma de Mexico and UNESCO, Mexico City, 1958.Google Scholar

References

  1. 1.
    G. Bredon, Sheaf Theory, McGraw-Hill, New York, 1967.zbMATHGoogle Scholar
  2. 2.
    E. H. Brown, Abstract homotopy theory, Trans. Amer. Math. Soc. 119 (1965), pp. 79–85.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    R. Godement, Topologie Algebrique et Theorie des Faisceaux, Hermann, Paris, 1958.zbMATHGoogle Scholar
  4. 4.
    A. Haefliger, Homotopy and integrability, Lecture Notes in Mathematics, No. 197, Springer-Verlag, New York, 1971, pp. 133–163.zbMATHGoogle Scholar
  5. 5.
    A. Haefliger, Feuilletages sur les variétés ouvertes, Topology 9 (1970), pp. 183–194.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    D. Husemoller, Fibre Bundles, McGraw-Hill, New York, 1966.CrossRefzbMATHGoogle Scholar
  7. 7.
    G. Segal, Classifying spaces and spectral sequences, Institut des Hautes Etudes Scientifiques, Publications Mathematiques, No. 34 (1968), pp. 105–112.Google Scholar

References

  1. 1.
    G. Segal, Classifying spaces and spectral sequences, Institut des Hautes Études Scientifiques, Publications Mathematiques, No. 34 (1968), pp. 105–112.Google Scholar

References

  1. 1.
    A. Haefliger, Feuilletages sur les variétés ouvertes, Topology 9 (1970), pp. 183–194.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    V. Poenaru, Homotopy theory and differentiable singularities, Lecture Notes in Mathematics, No. 197, Springer-Verlag, N. Y., 1971, pp. 106–132.zbMATHGoogle Scholar

References

  1. 1a.
    A. Haefliger, Feuilletages sur les variétés ouvertes, Topology 9 (1970), pp. 183–194.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, 1963, Interscience Publishers, New York.zbMATHGoogle Scholar
  3. 3.
    A. Phillips, Submersions of open manifolds, Topology 6 (1967), 171–206.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4a.
    A. Weil, Sur les théorèmes de de Rham, Comment. Math. Helv., 26 (1952), pp. 119–145.MathSciNetCrossRefzbMATHGoogle Scholar

References

  1. 1.
    K. Hoffman and R. Kunze, Linear Algebra, Prentice-Hall, Englewood Cliffs, N. J., 1961.zbMATHGoogle Scholar
  2. 2.
    D. Husemoller, Fibre Bundles, McGraw-Hill, New York, 1966.CrossRefzbMATHGoogle Scholar

References

  1. 1.
    A. Dold, Halbexakte Homotopiefunktoren, Lecture Notes in Math., no. 12, Springer-Verlag, Berlin and New York, 1966.zbMATHGoogle Scholar
  2. 2.
    A. Dold and R. Lashof, Principal quasi-fibrations and fibre homotopy equivalence of bundles, Illinois J. Math. 3 (1959), 285–305.MathSciNetzbMATHGoogle Scholar
  3. 3.
    S. MacLane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963.Google Scholar
  4. 4.
    _____, Milgram's classifying space as a tensor product of functors, Steenrod Conference, Lecture Notes in Math., no.168, Springer-Verlag, Berlin and New York.Google Scholar
  5. 5.
    R. Milgram, The bar construction and abelian H-spaces, Illinois J. Math. 11 (1967), 242–250.MathSciNetzbMATHGoogle Scholar
  6. 6.
    J. Milnor, Construction of universal bundles. II, Ann. of Math. (2) 63 (1956), 430–436.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    J.D. Stasheff, A classification theorem for fibre spaces, Topology 2 (1963), 239–246.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    _____, Associated fibre spaces, Michigan Math. J. 15 (1968), 457–470.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    _____, H-spaces and classifying spaces, Proc. Symp. Pure Math. 22, AMS, 1971.Google Scholar
  10. 10.
    _____, Homotopy associativity of H-spaces, I, II, Trans. Amer. Math. Soc. 108 (1963), 275–312.MathSciNetCrossRefzbMATHGoogle Scholar

References

  1. 1.
    A. Dold, Halbexakte Homotopiefunktorem, Lecture Notes in Math, No. 12, Springer-Verlag, Berlin and New York, 1966.zbMATHGoogle Scholar
  2. 2.
    _____, Partitions of unity in the theory of fibrations, Ann. of Math. (2) 78 (1963), 223–228.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    D. Husemoller, Fibre Bundles, McGraw-Hill, New York, 1966.CrossRefzbMATHGoogle Scholar
  4. 4.
    G. Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math., No. 34 (1968), 105–112.Google Scholar
  5. 5.
    J.D. Stasheff, A classification theorem for fibre spaces, Topology 2 (1963), 239–246.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    _____, H-spaces from a homotopy point of view, Lecture Notes in Math, 161, Springer-Verlag, Berlin and New York, 1970.zbMATHGoogle Scholar
  7. 7.
    J. Wirth, Fibre spaces and the higher homotopy cocycle relations, Thesis, Notre Dame, Ind., 1964.Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Raoul Bott

There are no affiliations available

Personalised recommendations