Constructing and Cataloging 2-Adjacent Knots
Geometric Topology
2025-10-02 v1
Abstract
Generalizing unknotting number, -adjacent knots have crossings such that changing any non-empty subset of them results in the unknot. In this paper, we determine the 2-adjacent knots through 12 crossings. Using Heegaard Floer -invariants and the Alexander polynomial, we develop a new technique to obstruct 2-adjacency, and we prove conjectures of Ito and Kato regarding 2-adjacent knots.
Cite
@article{arxiv.2510.00291,
title = {Constructing and Cataloging 2-Adjacent Knots},
author = {John Carney and Everett Meike},
journal= {arXiv preprint arXiv:2510.00291},
year = {2025}
}
Comments
23 pages, 8 figures