Abstract
Given a connection ω in aG-bundle overS2, then a process called radial trivialization from the poles gives a unique clutching function, i.e., an element γ of the loop group ΩG. Up to gauge equivalence, ω is completely determined by γ and a map f:S2 →g into the Lie algebra. Moreover, the Yang-Mills function of ω is the sum of the energy of γ and the square of a certain norm off. In particular, the Yang-Mills functional has the same Morse theory as the energy functional on ΩG. There is a similar description of connections in aG-bundle over an arbitrary Riemann surface, but so far not of the Yang-Mills functional.
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