On connections on principal bundles
Abstract
A new construction of a universal connection was given in BHS. The main aim here is to explain this construction. A theorem of Atiyah and Weil says that a holomorphic vector bundle E over a compact Riemann surface admits a holomorphic connection if and only if the degree of every direct summand of E is degree. In AB, this criterion was generalized to principal bundles on compact Riemann surfaces. This criterion for principal bundles is also explained.
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