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Ehresmann connections; covariant derivatives; connections on vector bundles, principal bundles, ∞-bundles, submersions, bundle gerbes; holonomy and higher holonomy; parallel transport; torsion; curvature. See also the tags [principal-bundles], [vector-bundles], [gerbes], [curvature], [geodesics], [characteristic-classes], [torsion].

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Definition of Connection as G-invariant splitting of a sequence which is a pulled back seque...

I'm reading Atiyah-Bott's paper "The Yang-Mills equations over Riemann surfaces" and have a couple of questions on page 547. They define a connection $A$ as a $G$-invariant splitting of the exact sequ …