Homotopy Theory of Principal Fibre Bundles. Classification

  • Gerd RudolphEmail author
  • Matthias Schmidt
Part of the Theoretical and Mathematical Physics book series (TMP)


We start with a discussion of fibrations and their exact homotopy sequence. Then, we classify principal bundles with a given structure group and a given base manifold up to vertical isomorphisms in terms of homotopy classes of mappings to the base space of a universal principal bundle. The classification carries over to vector bundles. Finally, we discuss universal connections.

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsUniversity of LeipzigLeipzigGermany

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