On complements of codimension-3 embeddings in \(S^ n\)
type: Item
instance of: scholarly article
title: On complements of codimension-3 embeddings in \(S^ n\)
zbMATH Open document ID: 0668.57020
DOI: 10.1016/0166-8641(89)90082-5
author: Steve Ferry
author: Erik K. Pedersen
author: Pierre Vogel
published in: Topology and its Applications
publication date: 1989-01-01T00:00:00Z
review text: This paper explores which groups can be realized as fundamental groups of complements of wildly embedded codimension 3 polyhedra in \(S^ n\), where \(n\geq 7\). The main theorem is the following. Let K be any finite polyhedron, \(1\leq \dim K\leq n-3\), which admits a PL embedding into \(S^ n\), and let \(\pi\) be a countably generated group. Then there exists an (in general non PL) embedding j: \(K\to S^ n\) with \(\pi_ 1(S^ n- j(K))\approx \pi\) if and only if \(\pi\) is perfect and \(H_ 2(\pi)=0\). The proof makes use of techniques from shape theory and decomposition theory.
Mathematics Subject Classification ID: 57N35
Mathematics Subject Classification ID: 57N45
Mathematics Subject Classification ID: 57Q35
zbMATH DE Number: 4094408
zbMATH Keywords: perfect group
zbMATH Keywords: fundamental groups of complements of wildly embedded codimension 3 polyhedra in \(S^ n\)
zbMATH Keywords: shape theory
zbMATH Keywords: decomposition theory
reviewed by: Peter Mrozik
MaRDI profile type: Publication
full work available at URL: 0166-8641(89)90082-5
OpenAlex ID: W2030601754
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description: scientific article; zbMATH DE number 4094408