Independence of Iterated Whitehead Doubles

TL;DR

This paper demonstrates that certain iterated Whitehead doubles of positive torus knots form an infinite family that are independent in the smooth concordance group, using 4-dimensional topology and previous homology cobordism results.

Contribution

It introduces new infinite families of knots with independent iterated Whitehead doubles in the smooth concordance group, extending previous independence criteria.

Findings

Infinite families of positive torus knots with independent iterated Whitehead doubles.

Application of 4-dimensional constructions to knot concordance.

Extension of homology cobordism independence results to knot theory.

Abstract

A theorem of Furuta and Fintushel-Stern provides a criterion for a collection of Seifert fibred homology spheres to be independent in the homology cobordism group of oriented homology 3-spheres. In this article we use these results and some 4-dimensional constructions to produce infinite families of positive torus knots whose iterated Whitehead doubles are independent in the smooth concordance group.