A remark on the Lewark–Zibrowius invariant

Mihai Marian

Vol. 339 (2025), No. 1, 191–200

DOI: 10.2140/pjm.2025.339.191

Abstract

We prove a conjecture about the concordance invariant $𝜗$, defined in a recent paper by Lewark and Zibrowius. This result simplifies the relation between $𝜗$ and Rasmussen’s $s$-invariant. The proof relies on Bar-Natan’s tangle version of Khovanov homology or, more precisely, on its distillation in the case of 4-ended tangles into the immersed curve theory of Kotelskiy, Watson and Zibrowius.

Keywords

Bar-Natan homology, $s$-invariant, tangles

Mathematical Subject Classification

Primary: 57K18

Milestones

Received: 28 May 2025

Revised: 1 July 2025

Accepted: 5 August 2025

Published: 1 September 2025