Non-slice linear combinations of iterated torus knots

TL;DR

This paper demonstrates that certain algebraic knots are linearly independent in the knot concordance group using twisted Blanchfield pairings, addressing a question posed by Rudolph in 1976.

Contribution

It introduces a novel application of twisted Blanchfield pairings to establish linear independence of large families of algebraic knots in the concordance group.

Findings

Confirmed linear independence of new algebraic knot families

Extended understanding of knot concordance group structure

Provided a new method for analyzing algebraic knots

Abstract

In 1976, Rudolph asked whether algebraic knots are linearly independent in the knot concordance group. This paper uses twisted Blanchfield pairings to answer this question in the affirmative for new large families of algebraic knots.