The algebraic characterization of the exteriors of certain 2-knots
type: Item
instance of: scholarly article
title: The algebraic characterization of the exteriors of certain 2-knots
zbMATH Open document ID: 0683.57008
DOI: 10.1007/BF01850660
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143698
review text: Working with TOP locally flat 2-knots, the author considers what algebraic information is needed to determine a 2-knot up to orientation and the ambiguity noted by Gluck (that there are at most two 2-knots with homeomorphic exteriors). Applying work of Freedman to the 4-manifold obtained by surgery on a knot with virtually solvable group, he obtains various results: in particular, that the Cappell-Shaneson knots are determined by their groups alone, modulo the Gluck ambiguity.
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 57N35
zbMATH DE Number: 4119256
zbMATH Keywords: knot exterior
zbMATH Keywords: locally flat 2-knots
zbMATH Keywords: homeomorphic exteriors
zbMATH Keywords: virtually solvable group
zbMATH Keywords: Cappell-Shaneson knots
zbMATH Keywords: Gluck ambiguity
author: Jonathan A. Hillman
reviewed by: C. Kearton
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4119256