Knot Logic and Arborescent Links
Geometric Topology
2025-05-20 v1
Abstract
This paper introduces a new algebra, the crossing algebra, that is applied to count the number of components for arborescent knots, links, tangles or states (of a state polynomial expansion such as the Kauffman bracket). This algebra is foundational, and it is related to generalisations of boolean logic and to aspects of foundations based in diagrams and networks. Applications are given to rational knots, links and tangles and to the structure of the bracket polynomial and the beginnings of Khovanov homology.
Keywords
Cite
@article{arxiv.2505.12722,
title = {Knot Logic and Arborescent Links},
author = {Louis H Kauffman},
journal= {arXiv preprint arXiv:2505.12722},
year = {2025}
}
Comments
51 pages, 39 diagrams, LaTeX document