Corrigendum to: “Unfoldings in knot theory”. (English) Zbl 0675.57011

Neumann, Walter; Rudolph, Lee

Math. Ann. 282, No. 2, 349-351 (1988).

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.

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

Keywords:

Unfoldings; polynomial maps; Milnor fibration; link at infinity; regular at infinity

References:

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