Cobordism of algebraic knots via Seifert forms
type: Item
instance of: scholarly article
title: Cobordism of algebraic knots via Seifert forms
zbMATH Open document ID: 0789.57015
DOI: 10.1007/BF01231284
author: Françoise Michel
author: P. Dubois
published in: Inventiones Mathematicae
publication date: 1993-08-17T00:00:00Z
full work available at URL: https://eudml.org/doc/144074
review text: An algebraic \((2n-1)\)-knot \(k\) is obtained as the link of an isolated singularity of a complex hypersurface in \(\mathbb{C}^{n+1}\), where the link is a topological \((2n-1)\)-sphere. In this paper the authors answer a question of Durfee: Are cobordant algebraic knots isotopic? For any \(n\geq 3\), the answer is no. The counter-examples are obtained by examining the Seifert forms of polynomials of the form \(g(z_ 0,z_ 1)+ z_ 2^ p+ z_ 3^ q+ z_ 4^ 2+\cdots+ z_ n^ 2\) for suitable \(g\), \(p\), \(q\), and using the Thom-Sebastiani theorem.
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14J70
zbMATH DE Number: 179519
zbMATH Keywords: Milnor fibre
zbMATH Keywords: isotopic knots
zbMATH Keywords: algebraic \((2n-1)\)-knot
zbMATH Keywords: link of an isolated singularity of a complex hypersurface
zbMATH Keywords: cobordant algebraic knots
zbMATH Keywords: Seifert forms
reviewed by: C. Kearton
MaRDI profile type: Publication
cites work: Sur la monodromie des singularites isolees d'hypersurfaces complexes
cites work: Fibered knots and algebraic singularities
cites work: Q3980868
cites work: Knot cobordism groups in codimension two
cites work: Singular Points of Complex Hypersurfaces. (AM-61)
cites work: The Seifert matrices of Milnor fiberings defined by holomorphic functions
cites work: Un résultat sur la monodromie. (A result on the monodromy)
cites work: Cobordism of algebraic knots
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description: scientific article; zbMATH DE number 179519