Cobordism of algebraic knots via Seifert forms
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.
link of an isolated singularity of a complex hypersurface
scientific article; zbMATH DE number 179519
scientific article