Homotopy is not isotopy for homeomorphisms of 3-manifolds
type: Item
instance of: scholarly article
title: Homotopy is not isotopy for homeomorphisms of 3-manifolds
zbMATH Open document ID: 0596.57008
DOI: 10.1016/0040-9383(86)90003-0
author: John L. Friedman
author: D. M. Witt
published in: Topology
publication date: 1986-01-01T00:00:00Z
review text: It has been conjectured for a long time that there is no homeomorphism of a closed 3-manifold which is homotopic but not isotopic to the identity. The authors give in this paper the first counterexample known to this conjecture. This counterexample occurs for the connected sum of two 3- manifolds obtained as quotients of \(S^ 3\) by certain finite subgroups of SO(4); the homeomorphism considered is a Dehn twist along the sphere of connected sum. Motivated by certain problems in quantum gravity, the authors also determine the group of isotopy classes of homeomorphisms fixing a point (resp. a ball) for 3-manifolds of this type.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57R52
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 57R50
zbMATH DE Number: 3960564
zbMATH Keywords: homeomorphism of a closed 3-manifold
zbMATH Keywords: homotopic but not isotopic to the identity
zbMATH Keywords: connected sum of two 3-manifolds
zbMATH Keywords: Dehn twist
zbMATH Keywords: quantum gravity
zbMATH Keywords: isotopy classes of homeomorphisms
reviewed by: Francis Bonahon
MaRDI profile type: Publication
full work available at URL: 0040-9383(86)90003-0
OpenAlex ID: W2040357980
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description: scientific article; zbMATH DE number 3960564