The Oka principle for sections of stratified fiber bundles

摘要

Let Y be a complex manifold with the property that every holomorphic map from a neighborhood of a compact convex set K in a complex Euclidean space ? ~n to Y can be approximated, uniformly on K, by entire maps ? ~n → Y. If X is a reduced Stein space and π: Z → X is a holomorphic fiber bundle with fiber Y then we show that sections X → Z satisfy the Oka principle with approximation and interpolation. The analogous result is proved for sections of stratified fiber bundles, and of submersions with stratified sprays over Stein spaces.