Applications of a Parametric Oka Principle for Liftings

Abstract

A parametric Oka principle for liftings, recently proved by Forstnerič, provides many examples of holomorphic maps that are fibrations in a model structure introduced in previous work of the author. 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 ℂⁿ extends holomorphically to ℂⁿ.