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arXiv · 1608.02400

On connections on principal bundles

Indranil Biswas
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Abstract

A new construction of a universal connection was given in \cite{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 \cite{AB}, this criterion was generalized to principal bundles on compact Riemann surfaces. This criterion for principal bundles is also explained.

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Indranil Biswas. 2016-08-08. On connections on principal bundles. https://arxiv.org/abs/1608.02400

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