Complements of Runge domains and holomorphic hulls
type: Item
instance of: scholarly article
title: Complements of Runge domains and holomorphic hulls
zbMATH Open document ID: 0811.32007
published in: Michigan Mathematical Journal
publication date: 1995-05-02T00:00:00Z
review text: The author obtains new general topological properties of complements of a holomorphically convex subset \(A \subset X\) in a Stein manifold \(X\) of dimension \(n \geq 2\). Let us formulate one of his results. Theorem 1. If \(A \subset \mathbb{C}^ n\) \((n \geq 2)\) is either a polynomially convex of \(\mathbb{C}^ n\) or the closure \(A = \overline{\Omega}\) of a bounded pseudoconvex Runge domain \(\Omega \subset \mathbb{C}^ n\) with \(C^ 1\) boundary, then the complement of \(A\) is \((n - 1)\)-connected: \[ \pi_ k(\mathbb{C}^ n \setminus A) = 0,\quad 1 \leq k \leq n - 1, \] and for any abelian group \(G\) \[ H_ k(\mathbb{C}^ n \setminus A; G) = 0,\quad 1 \leq k \leq n - 1. \]
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32E99
Mathematics Subject Classification ID: 32E20
zbMATH DE Number: 682544
zbMATH Keywords: holomorphic hulls
zbMATH Keywords: Stein manifold
zbMATH Keywords: Runge domain
author: Franc Forstnerič
reviewed by: P. Z. Agranovich
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004997
OpenAlex ID: W2053307142
DOI: 10.1307/MMJ/1029004997
description: scientific article; zbMATH DE number 682544