Universal Knot Diagrams
Geometric Topology
2019-11-06 v4 Combinatorics
Abstract
We study collections of planar curves that yield diagrams for all knots. In particular, we show that a very special class called potholder curves carries all knots. This has implications for realizing all knots and links as special types of meanders and braids. We also introduce and apply a method to compare the efficiency of various classes of curves that represent all knots.
Keywords
Cite
@article{arxiv.1804.09860,
title = {Universal Knot Diagrams},
author = {Chaim Even-Zohar and Joel Hass and Nati Linial and Tahl Nowik},
journal= {arXiv preprint arXiv:1804.09860},
year = {2019}
}