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The homotopy principle in complex analysis: a survey

Franc Forstneric
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Abstract

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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Franc Forstneric. 2003-03-03. The homotopy principle in complex analysis: a survey. https://arxiv.org/abs/math/0301067

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