The Oka principle for sections of stratified fiber bundles

Abstract

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 C n to Y can be approximated, uniformly on K, by entire maps C 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.