2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229209A parametric Oka principle for liftings, recently proved by Forstneric, provides many examples of holomorphic maps that are fibrations in a model structure introduced in previous work of ours. We use this to show that the basic Oka property is equivalent to the parametric Oka property for a large class of manifolds. We introduce new versions of the basic and parametric Oka properties and show, for example, that a complex manifold $X$ has the basic Oka property if and only if every holomorphic map to $X$ from a contractible submanifold of $\mathbb C^n$ extends holomorphically to $\mathbb C^n$.A few minor improvements in version 2. To appear in a volume in honour of Linda P. Rothschild, Trends in Mathematics series, BirkhauserComplex VariablesAlgebraic Topology32Q28 (Primary); 18F20, 18G55, 32E10, 55U35 (Secondary)text