A relative Oka-Grauert principle on 1-convex spaces

Leiterer, Jürgen; Vâjâitu, Viorel

doi:10.1515/crll.2003.095

“…This general version of the Oka principle has recently been used by Ivarsson and Kutzschebauch [37] in a solution of the holomorphic Vaserstein problem posed by Gromov in [31]. Some recent extensions of the Oka principle should be mentioned: For sections of subelliptic holomorphic submersions over 1-convex manifolds (see Prezelj [45]); for sections of holomorphic Banach bundles over 1-convex manifolds (Leiterer and Vâjâitu [41]); and the soft Oka principle to the effect that the Oka principle holds universally if one allows homotopic deformations of the Stein structure on the source manifold (see [24,25]).…”

Section: Introductionmentioning

confidence: 99%

The Oka Principle for Sections of Stratified Fiber Bundles

Forstnerič¹

2010

Pure and Applied Mathematics Quarterly

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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.

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“…Some recent extensions of the Oka principle should be mentioned: For sections of subelliptic holomorphic submersions over 1-convex manifolds (see Prezelj [44]); for sections of holomorphic Banach bundles over 1-convex manifolds (Leiterer and Vâjâitu [40]); and the soft Oka principle to the effect that the Oka principle holds universally if one allows homotopic deformations of the Stein structure on the source manifold (see [23,24]).…”

Section: Introductionmentioning

confidence: 99%

The Oka principle for sections of stratified fiber bundles

Forstnerič¹

2007

Preprint

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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.

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