Cobordism of algebraic knots defined by Brieskorn polynomials

TL;DR

This paper investigates when algebraic knots derived from Brieskorn polynomials are cobordant, establishing that cobordism occurs precisely when the polynomials share the same exponents, thus linking knot cobordism to polynomial invariants.

Contribution

It provides a complete characterization of cobordism classes of algebraic knots associated with Brieskorn polynomials based on their exponents.

Findings

Cobordism of algebraic knots is characterized by polynomial exponents.

Cobordant algebraic knots correspond to polynomials with identical exponents.

The result applies under certain assumptions on the polynomials.

Abstract

In this paper we study the cobordism of algebraic knots associated with weighted homogeneous polynomials, and in particular Brieskorn polynomials. Under some assumptions we prove that the associated algebraic knots are cobordant if and only if the Brieskorn polynomials have the same exponents.