A Discrete Theory of Connections on Principal Bundles

  title={A Discrete Theory of Connections on Principal Bundles},
  author={Melvin Leok},
Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing the discrete analogue of the Atiyah sequence, with a connection corresponding to the choice of a splitting of the short exact sequence. Equivalent representations of a discrete connection are considered, and an extension of the pair groupoid composition… CONTINUE READING
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