2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71477A Stein covering of a complex manifold may be used to realise its analytic cohomology in accordance with the Cech theory. If, however, the Stein covering is parameterised by a smooth manifold rather than just a discrete set, then we construct a cohomology theory in which an exterior derivative replaces the usual combinatorial Cech differential. Our construction is motivated by integral geometry and the representation theory of Lie groups.15 pagesComplex VariablesPrimary 32L10; Secondary 22E46, 32L25, 43A85text