Cobordism of algebraic knots defined by Brieskorn polynomials, II

Vincent Blanloeil; Osamu Saeki

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arXiv · 2411.03662

Cobordism of algebraic knots defined by Brieskorn polynomials, II

Vincent Blanloeil·Osamu Saeki

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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 type 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. As a corollary, we show that a spherical algebraic knot associated with a Brieskorn polynomial has infinite order in the knot cobordism group.

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BibTeX RIS

Vincent Blanloeil, Osamu Saeki. 2024-11-06. Cobordism of algebraic knots defined by Brieskorn polynomials, II. https://arxiv.org/abs/2411.03662

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