Applications of a parametric Oka principle for liftings

Details Applications of a parametric Oka principle for liftings Applications of a parametric Oka principle for liftings

2009-01-28

arxiv.org/abs/0901.4388v2

Mathematics

Complex Variables

A few minor improvements in version 2. To appear in a volume in honour of Linda P. Rothschild, Trends in Mathematics series, B

Scientific paper

A 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 $\mathbb C^n$.

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