\(\overline{\partial}\)-free maps satisfy the homotopy principle
type: Item
instance of: scholarly article
title: \(\overline{\partial}\)-free maps satisfy the homotopy principle
zbMATH Open document ID: 0936.32009
DOI: 10.1016/S0019-3577(97)87569-6
published in: Indagationes Mathematicae. New Series
publication date: 2000-05-14T00:00:00Z
review text: Using Gromov's method of convex integration the author proves that the space of all \(\bar\partial\)-free maps of any complex manifold \(V\) in \(\mathbb{C}^n\) is homotopically equivalent to the space of all sections of the corresponding bundle in the space of jets of smooth maps \(f:V\to \mathbb{C}^n\).
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 58A20
Mathematics Subject Classification ID: 58D99
Mathematics Subject Classification ID: 32A10
Mathematics Subject Classification ID: 58D05
Mathematics Subject Classification ID: 58C10
zbMATH DE Number: 1251253
zbMATH Keywords: homotopy equivalence
zbMATH Keywords: convex integration
author: Boris Shapiro
reviewed by: Valery Borisovich Marenich
MaRDI profile type: Publication
cites work: Affine Gelfand-Dickey brackets and holomorphic vector bundles
cites work: Partial Differential Relations
cites work: Nondegenerate curves on \(S^ 2\) and orbit classification of the Zamolodchikov algebra
cites work: Q4924941
cites work: Applications of convex integration to symplectic and contact geometry
cites work: Topology of the space of nondegenerate curves
cites work: Symplectic leaves of the Gel'fand-Dikij brackets and homotopy classes of nondegenerate curves
cites work: On the number of connected components in the space of closed nondegenerate curves on 𝑆_{𝑛}
description: scientific article; zbMATH DE number 1251253