Filtered Instantons and the Concordance of Satellites

TL;DR

This paper introduces new invariants for integer homology spheres using filtered instanton homology and applies these to establish results on knot concordance, including satellite knot independence.

Contribution

It develops criteria for satellite knot independence and demonstrates the independence of the Whitehead n-ble Pn using filtered instanton invariants.

Findings

Criteria for satellite knot linear independence

Proof of Whitehead n-ble Pn independence

Application of instanton invariants to knot concordance

Abstract

In \cite{NST23}, Nozaki-Sato-Taniguchi defined a family of invariants $ r_s $ for integer homology spheres with filtered instanton homology \cite{FS92}. Coupling these with techniques in classical knot theory, we produce some results in the knot concordance group, including criteria for a family of satellite knots to be linearly independent and the independence of what we call the Whitehead $ n $-ble $ P_n $.