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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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Chern class of a logarithmic connection
There exist a paper due to Makoto Ohtsuki about a Residue Formula for Chern Classes Associated with Logarithmic Connections:
http://projecteuclid.org/download/pdf_1/euclid.tjm/1270215030 …