Principal S1-bundles

  • David E. Blair
Part of the Progress in Mathematics book series (PM, volume 203)
Let P and M be C manifolds, π : PM a C map of P onto M and G a Lie group acting on P to the right. Then (P, G, M) is called a principal G-bundle if
  1. 1.

    G acts freely on P,

     
  2. 2.

    π(p 1) = π(p 2) if and only if there exists gG such that p 1 g = p 2,

     
  3. 3.

    P is locally trivial over M, i.e., for every mM there exists a neighborhood U of m and a map F u : π-1(U) → G such that F u (pg) = (F u (p))g and such that the map Ψ : π-1(U) → U × G taking p to (π(p), F u (p)) is a diffeomorphism.

     

Keywords

Short Exact Sequence Principal Bundle Connection Form Horizontal Lift Bundle Isomorphism 
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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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • David E. Blair
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

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