Corrigendum to: ``Unfoldings in knot theory''
type: Item
instance of: scholarly article
title: Corrigendum to: ``Unfoldings in knot theory''
zbMATH Open document ID: 0675.57011
DOI: 10.1007/BF01456981
author: L. Rudolph
author: Walter D. Neumann
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
review text: This paper corrects an error in the authors' ``Unfoldings in knot theory'' [reviewed above (see Zbl 0675.57010)]. In the original paper various theorems were stated about ``good'' polynomial maps f: \(C^ n\to C\) including the claim that the link at infinity always has a ``Milnor fibration''. The map \(f(x,y)=x^ 2y+x\) has no singularities but the link at infinity is not a fiberable link. The results of the original paper all hold with a modified definition of ``good''. The fiber \(f^{-1}(c)\) of f is regular if there is a neighborhood D of c in C such that \(f| f^{-1}(D): f^{-1}(D)\to D\) is a locally trivial \(C^{\infty}\) map and regular at infinity if there is a neighborhood D of c in C and a compact set K in \(C^ N\) such that \(f| f^{-1}(D)-K: f^{-1}(D)- K\to D\) is a locally trivial \(C^{\infty}\) fibration. The polynomial map f: \(C^ n\to C\) is good if every fiber is regular at infinity. Regular is equivalent to regular at infinity and non-singular.
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 14E25
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
zbMATH DE Number: 4105879
zbMATH Keywords: Unfoldings
zbMATH Keywords: polynomial maps
zbMATH Keywords: Milnor fibration
zbMATH Keywords: link at infinity
zbMATH Keywords: regular at infinity
Wikidata QID: Q60148883
reviewed by: George E. Lang jun.
MaRDI profile type: Publication
cites work: Unfoldings in knot theory
cites work: Propriétés topologiques des polynômes de deux variables complexes et automorphismes algébriques de l'espace \(C^2\)
cites work: On irreducible 3-manifolds which are sufficiently large
full work available at URL: https://doi.org/10.1007/bf01456981
OpenAlex ID: W2025608471
description: scientific article; zbMATH DE number 4105879