The homotopy principle in complex analysis: a survey

Details The homotopy principle in complex analysis: a survey The homotopy principle in complex analysis: a survey

2003-01-08

arxiv.org/abs/math/0301067v2

Contemporary Mathematics, 332 (2003), 73-99

Mathematics

Complex Variables

32 pages

Scientific paper

This is a survey on the homotopy principle in complex analysis on Stein manifolds, also called the Oka principle in this context. We concentrate on the following topics: the Oka-Grauert principle (classification of holomorphic vector bundles); the homotopy principle for holomorphic mappings from Stein manifolds and, more generally, for sections of holomorphic submersions with sprays; question on removability of intersections of holomorphic mappings with complex subvarieties; embeddings and immersions of Stein manifolds in affine spaces of minimal dimension; embeddings of open Riemann surfaces in the affine plane; noncritical holomorphic functions on Stein manifolds and the Oka principle for holomorphic submersions of Stein manifolds to affine spaces.

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