Manifolds, Vector Bundles, and Lie Groups

Part of the Applied Mathematical Sciences book series (AMS, volume 115)


This appendix provides background material on manifolds, vector bundles, and Lie groups, which are used throughout the book. We begin with a section on metric spaces and topological spaces, defining some terms that are necessary for the concept of a manifold, defined in §2, and for that of a vector bundle, defined in §3. These sections contain mostly definitions; however, a few results about compactness are proved.


Vector Bundle Irreducible Representation Unitary Representation Haar Measure Smooth Manifold 
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.


  1. Dug.
    J. Dugundji, Topology, Allyn and Bacon, New York, 1966.MATHGoogle Scholar
  2. GP.
    V. Guillemin and A. Pollack, Differential Topology, Prentice-Hall, Englewood-Cliffs, New Jersey, 1974.MATHGoogle Scholar
  3. HS.
    M. Hausner and J. Schwartz, Lie Groups; Lie Algebras, Gordon and Breach, London, 1968.MATHGoogle Scholar
  4. Helg.
    S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic, New York, 1978.MATHGoogle Scholar
  5. HT.
    R. Howe and E. Tan, Non-Abelian Harmonic Analysis, Springer, New York, 1992.MATHCrossRefGoogle Scholar
  6. Hus.
    D. Husemuller, Fibre Bundles, McGraw-Hill, New York, 1966.Google Scholar
  7. Kn.
    A. Knapp, Representation Theory of Semisimple Groups, Princeton University Press, Princeton, N. J., 1986.MATHGoogle Scholar
  8. Stb.
    S. Sternberg, Lectures on Differential Geometry, Prentice Hall, Englewood Cliffs, N. J., 1964.MATHGoogle Scholar
  9. Str.
    R. Strichartz, The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations, J. Funct. Anal. 72(1987), 320–345.Google Scholar
  10. T.
    M. Taylor, Noncommutative Harmonic Analysis, AMS, Providence, R. I., 1986.MATHGoogle Scholar
  11. Var1.
    V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, Springer, New York, 1984.MATHGoogle Scholar
  12. Var2.
    V. S. Varadarajan, An Introduction to Harmonic Analysis on Semisimple Lie Groups, Cambridge University Press, Cambridge, 1986.Google Scholar
  13. Wal1.
    N. Wallach, Harmonic Analysis on Homogeneous Spaces, Marcel Dekker, New York, 1973.MATHGoogle Scholar
  14. Wal2.
    N. Wallach, Real Reductive Groups, I, Academic, New York, 1988.MATHGoogle Scholar
  15. Wh.
    H. Whitney, Sphere spaces, Proc. NAS, USA 21(1939), 462–468.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

Personalised recommendations