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 and each of the 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