English

An instanton take on some knot detection results

Geometric Topology 2024-09-10 v2 Quantum Algebra

Abstract

We give new proofs that Khovanov homology detects the figure eight knot and the cinquefoils, and that HOMFLY homology detects 525_2 and each of the P(3,3,2n+1)P(-3,3,2n+1) pretzel knots. For all but the figure eight these mostly follow the same lines as in previous work. The key difference is that in honor of Tom Mrowka's 60th birthday, the arguments here use instanton Floer homology rather than knot Floer homology.

Keywords

Cite

@article{arxiv.2211.03743,
  title  = {An instanton take on some knot detection results},
  author = {John A. Baldwin and Steven Sivek},
  journal= {arXiv preprint arXiv:2211.03743},
  year   = {2024}
}

Comments

17 pages; written for the proceedings of "Frontiers in Geometry and Topology," a conference in honor of Tom Mrowka's 60th birthday. v2: accepted version

R2 v1 2026-06-28T05:21:15.710Z