English

Closures of $3$-braids and detection

Geometric Topology 2025-11-05 v2

Abstract

We give some new link detection results for link Floer homology, Khovanov homology and annular Khovanov homology. The links we detect arise via different closure operations on 33-braids. Examples of our results include that link Floer homology detects the Mazur link, that annular Khovanov homology detects the Mazur pattern, and that Khovanov homology detects L6a2 and L9n15. The Mazur pattern detection result depends on a new bound on the rank of the annular Khovanov homology of certain links.

Keywords

Cite

@article{arxiv.2407.11145,
  title  = {Closures of $3$-braids and detection},
  author = {Fraser Binns},
  journal= {arXiv preprint arXiv:2407.11145},
  year   = {2025}
}

Comments

31 pages, 4 figures. Incorporated referee comments, removed claim from Theorem 1.5 due to incomplete proof

R2 v1 2026-06-28T17:42:04.162Z