Oka's principle for holomorphic fiber bundles with sprays
By F. Forstnerič, Jasna Prezelj. 2000
54 citations recorded by the source corpus.
We give a proof of the following theorem of M. Gromov (Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc., 2 (1989), 851-897). Let Z be a holomorphic fiber bundle over a Stein manifold. If the fiber of Z admits a dominating holomorphic spray then the inclusion of the space of global holomorphic sections of Z into the space of continuous sections is a weak homotopy equivalence. In the classical case when the fiber is a complex Lie group or a homogeneous space this was proved by H. Grauert (Math. Ann., 135 (1958), 263--273). For further results in this direction see the papers math.CV/0101040, math.CV/0101040, math.CV/0101034, math.CV/0101238, math.CV/0107039, math.CV/0110201.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/361c2a76d84009c0451c129fc29b38ca4ae6f09e
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In Geometry and Topology
- F. Forstnerič
- Jasna Prezelj
- F. Kutzschebauch
- E. F. Wold
- F. Lárusson
- J. Fornaess
- S. Kaliman
- Björn Ivarsson
Citations in the corpus
- Survey of Oka theory (2010, unknown): “Prezelj and the first-named author in [21, 22, 23].”
- Holomorphic flexibility properties of complex manifolds (2004, background): “5 in [28] the restriction E|Ω → Ω admits the structure of a holomorphic vector bundle and a holomorphic direct sum splitting E|Ω = H⊕H′, where H′ is the kernel of ds at the zero section of E ([41], p.”
- Extending holomorphic sections from complex subvarieties (2001, methodology): “Proof. It suffices to apply the proof of Theorem 5.5 in [ FP1 ],but replacing Proposition 5.2 in [FP1] by Proposition 3.2 above.”