Rational Link Fertility
Geometric Topology
2023-03-29 v1
Abstract
A knot K is the resultant of a knot H if there exists a minimal crossing diagram D of K such that some crossings of D can be altered to produce H. K is fertile if every prime knot H with crossing number less than c(K) is a resultant of K. K is n-fertile if every prime knot H with crossing number less than n is a resultant of K. We classify the fertility and fertility number of all rational links. This requires the introduction of the analogous concept of link fertility.
Keywords
Cite
@article{arxiv.2303.15650,
title = {Rational Link Fertility},
author = {Andrew Ducharme},
journal= {arXiv preprint arXiv:2303.15650},
year = {2023}
}
Comments
27 pages, 5 figures, 13 tables