Gauge theory and Rasmussen's invariant

TL;DR

This paper revisits the relationship between Rasmussen's knot invariant s(K) and a gauge-theory counterpart, correcting previous errors and clarifying properties such as non-additivity under connected sums.

Contribution

It provides a corrected analysis of the gauge-theory interpretation of s(K), including a detailed corrigendum and clarification of its properties.

Findings

The original proof of s(K) equals the gauge-theory invariant contained errors.

The gauge-theory counterpart of s(K) is not additive under connected sums.

The paper clarifies which parts of the previous work remain valid.

Abstract

A previous paper of the authors' contained an error in the proof of a key claim, that Rasmussen's knot-invariant s(K) is equal to its gauge-theory counterpart. The original paper is included here together with a corrigendum, indicating which parts still stand and which do not. In particular, the gauge-theory counterpart of s(K) is not additive for connected sums.