Non-slice linear combinations of iterated torus 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.

Real Seifert forms, Hodge numbers and Blanchfield pairings

“…The methods of [BCP18], which we presented in this article, allow us to compute the Casson-Gordon signatures. As an application [BCP18] and later [CKP19] could prove non-sliceness of some linear combinations of iterated torus knots, generalizing previous results of Hedden, Kirk and Livingston [HKL12].…”