文摘
A new construction of a universal connection was given in Biswas, Hurtubise and Stasheff (2012). The main aim here is to explain this construction. A theorem of Atiyah and Weil says that a holomorphic vector bundle EE over a compact Riemann surface admits a holomorphic connection if and only if the degree of every direct summand of EE is zero. In Azad and Biswas (2002), this criterion was generalized to principal bundles on compact Riemann surfaces. This criterion for principal bundles is also explained.