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Nonslice linear combinations of iterated torus knots

Anthony Conway, Min Hoon Kim and Wojciech Politarczyk

Algebraic & Geometric Topology 23 (2023) 765–802
Abstract

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

Keywords
knot, concordance, algebraic knot, iterated torus knot, Casson–Gordon invariants, twisted Blanchfield form
Mathematical Subject Classification
Primary: 57K10
References
Publication
Received: 29 November 2020
Revised: 13 August 2021
Accepted: 18 September 2021
Published: 9 May 2023
Authors
Anthony Conway
Max-Planck-Institut für Mathematik
Bonn
Germany
Massachusetts Institute of Technology
Cambridge, MA
United States
Min Hoon Kim
Department of Mathematics Education
Kyungpook National University
Daegu
South Korea
Wojciech Politarczyk
Institute of Mathematics
University of Warsaw
Warszawa
Poland

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