Cobordism of algebraic knots defined by Brieskorn polynomials, II

Vincent Blanlœil and Osamu Saeki

Journal of Singularities
volume 29 (2026), 149-174

Received: 10 November 2024. In revised form: 6 May 2026

DOI: 10.5427/jsing.2026.29f


Abstract:

In our previous paper, we obtained several results concerning cobordisms of algebraic knots associated with Brieskorn polynomials: for example, under certain conditions, we showed that the exponents are cobordism invariants. In this paper, we further obtain new results concerning the Fox-Milnor relations, decomposition of the algebraic cobordism class of an algebraic knot associated with a Brieskorn polynomial that has a null-cobordant factor over the field of rational numbers, and cyclic suspensions of knots. We also show that a certain infinite family of spherical algebraic knots associated with Brieskorn polynomials are linearly independent in the knot cobordism group.


2020 Mathematical Subject Classification:

Primary 57K45; Secondary 32S55, 57K10


Key words and phrases:

Algebraic knot, Brieskorn polynomial, cobordism, Fox-Milnor relation, algebraic cobordism group, cyclic suspension


Author(s) information:

V. Blanlœil
UFR Mathématique et Informatique, IRMA
Université de Strasbourg
7, rue René Descartes
F-67084 Strasbourg, France
email: v.blanloeil@math.unistra.fr

O. Saeki
Institute of Mathematics for Industry
Kyushu University
Motooka 744
Nishi-ku, Fukuoka 819-0395, Japan
email: saeki@imi.kyushu-u.ac.jp