On connections on principal bundles
Copyright policy )On connections on principal bundles
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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Mathematics - Differential Geometry, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), Principal bundle, Holomorphic connection, Real Higgs bundle, principal bundle, 53C05, 53C07, 32L05, holomorphic connection, Differential Geometry (math.DG), Holomorphic bundles and generalizations, real Higgs bundle, QA1-939, FOS: Mathematics, Universal connection, universal connection, Mathematics, Connections (general theory)
Mathematics - Differential Geometry, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), Principal bundle, Holomorphic connection, Real Higgs bundle, principal bundle, 53C05, 53C07, 32L05, holomorphic connection, Differential Geometry (math.DG), Holomorphic bundles and generalizations, real Higgs bundle, QA1-939, FOS: Mathematics, Universal connection, universal connection, Mathematics, Connections (general theory)
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