Rasmussen s-invariants of satellites do not detect slice knots

TL;DR

This paper shows that for many knots, the Rasmussen s-invariants of their satellite knots cannot determine if they are slice, answering a previously open question in knot theory.

Contribution

It demonstrates that Rasmussen s-invariants fail to detect sliceness in a broad class of satellite knots, providing new insights into their limitations.

Findings

Rasmussen s-invariants do not detect sliceness in many satellite knots.

Answers Hedden's question negatively.

Relies on Kronheimer-Mrowka and Cochran-Harvey-Horn's work.

Abstract

We present a large family of knots for which the Rasmussen s-invariants of arbitrary satellites do not detect sliceness. This answers a question of Hedden. The proof hinges on work of Kronheimer-Mrowka and Cochran-Harvey-Horn.