Gauss–Manin connection
= Gauss–Manin connection
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{title2=$\nabla:\mathcal H\to\mathcal H\otimes\Omega_S^1$}
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The flat connection on the complexified fibre-cohomology <local system> differentiates cohomology classes using topological parallel transport. For a smooth proper holomorphic family, relative de Rham cohomology identifies it with the connecting morphism obtained by retaining one base differential in the absolute de Rham complex.