English

A Remark on the Lewark-Zibrowius Invariant

Geometric Topology 2025-09-16 v2

Abstract

We prove a conjecture about the concordance invariant ϑ\vartheta, defined in a recent paper by Lewark and Zibrowius. This result simplifies the relation between ϑ\vartheta and Rasmussen's ss-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-Zibrowius.

Keywords

Cite

@article{arxiv.2503.17854,
  title  = {A Remark on the Lewark-Zibrowius Invariant},
  author = {Mihai Marian},
  journal= {arXiv preprint arXiv:2503.17854},
  year   = {2025}
}

Comments

8 pages, 4 figures. v2: Equivalent to published version, erased a false claim in Corollary 1.2

R2 v1 2026-06-28T22:31:01.232Z