Homology of Fibrations

  • Jean Dieudonné
Part of the Modern Birkhäuser Classics book series (MBC)


In 1935, at the instigation of Hopf, his student Stiefel undertook in his dissertation [457] to extend Hopf’s work on vector fields (Part 2, chap. Ill, §3). Given an n-dimensional compact C manifold M, the problem was to investigate whether there exists on M, not only one nowhere vanishing vector field, but a system of m vector fieldsXj (1≤j≤m) for some mn, subject to the condition that at each point x ∈ M, the m tangent vectors Xj(x) are linearly independent (hence≠0). The case m = n is particularly interesting in differential geometry, because the existence of such systems of n vector fields is equivalent to the existence of a parallelism on M.


Vector Field Differential Geometry Tangent Vector Algebraic Topology Differential Topology 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  • Jean Dieudonné
    • 1
  1. 1.75015 ParisFrance

Personalised recommendations