Corrigendum to: “Unfoldings in knot theory”.

*(English)*Zbl 0675.57011This 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.

Reviewer: G.Lang

##### MSC:

57Q45 | Knots and links in high dimensions (PL-topology) (MSC2010) |

32S05 | Local complex singularities |

57M25 | Knots and links in the \(3\)-sphere (MSC2010) |

14E25 | Embeddings in algebraic geometry |

58C25 | Differentiable maps on manifolds |

58K99 | Theory of singularities and catastrophe theory |

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\textit{W. Neumann} and \textit{L. Rudolph}, Math. Ann. 282, No. 2, 349--351 (1988; Zbl 0675.57011)

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##### References:

[1] | Neumann, W., Rudolph, L.: Unfoldings in knot theory. Math. Ann.278, 409-439 (1987) · Zbl 0675.57010 · doi:10.1007/BF01458078 |

[2] | Neumann, W.: Complex algebraic plane curves via their links at infinity. Preprint (1988) |

[3] | Suzuki, M.: Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algébriques de l’espace 351-1. J. Math. Soc. Japan26, 241-257 (1974). · Zbl 0276.14001 · doi:10.2969/jmsj/02620241 |

[4] | Waldhausen, F.: On irreducible 3-manifolds that are sufficiently large. Ann. Math.87, 56-88 (1968) · Zbl 0157.30603 · doi:10.2307/1970594 |

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