Knot Fertility and Lineage
Geometric Topology
2017-05-26 v1
Abstract
In this paper, we introduce a new type of relation between knots called the descendant relation. One knot is a descendant of another knot if can be obtained from a minimal crossing diagram of by some number of crossing changes. We explore properties of the descendant relation and study how certain knots are related, paying particular attention to those knots, called fertile knots, that have a large number of descendants. Furthermore, we provide computational data related to various notions of knot fertility and propose several open questions for future exploration.
Keywords
Cite
@article{arxiv.1705.08990,
title = {Knot Fertility and Lineage},
author = {Jason Cantarella and Allison Henrich and Elsa Magness and Oliver O'Keefe and Kayla Perez and Eric J. Rawdon and Briana Zimmer},
journal= {arXiv preprint arXiv:1705.08990},
year = {2017}
}
Comments
20 pages, 11 figures, 14 tables