Cobordism of algebraic knots defined by Brieskorn polynomials, II
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.
Keywords
Cite
@article{arxiv.2411.03662,
title = {Cobordism of algebraic knots defined by Brieskorn polynomials, II},
author = {Vincent Blanloeil and Osamu Saeki},
journal= {arXiv preprint arXiv:2411.03662},
year = {2025}
}
Comments
25 pages, 2 figures. Some background materials and lemmas together with their proofs have been added