Knotted contractible 4-manifolds in \(S^4\).
type: Item
instance of: scholarly article
title: Knotted contractible 4-manifolds in \(S^4\).
zbMATH Open document ID: 1052.57032
published in: Pacific Journal of Mathematics
publication date: 2004-09-16T00:00:00Z
review text: The author studies the possibility of knotting of a contractible polyhedron in a PL manifold in codimension zero and shows by examples that this phenomenon occurs on the level of 4-manifolds. This is realised by a construction of two piecewise linear (or smooth) embeddings, \(e_0\) and \(e_1\) of a certain compact contractible 4-manifold \(M\) into \(S^4\) such that \(\pi_1(S^4\setminus e_1(M))\) is nontrivial and \(\pi_1(S^4\setminus e_0(M))\) is trivial. Since \(e_0\) is homotopic to \(e_1\), the manifold \(M\) knots in \(S^4\). In addition, it is proved that any finitely presented perfect group with a balanced presentation is a knot group of an embedding of some contractible 4-manifold in \(S^4\).
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 57N35
zbMATH DE Number: 2101053
zbMATH Keywords: knotting
zbMATH Keywords: contractible four manifold
reviewed by: Ivan Ivanšić
MaRDI profile type: Publication
full work available at URL: pjm.2003.208.283
OpenAlex ID: W2026367875
DOI: 10.2140/PJM.2003.208.283
author: W. B. Raymond Lickorish
description: scientific article; zbMATH DE number 2101053