A New Way to Tabulate Knots
几何拓扑
2007-05-23 v1
摘要
We introduce a new way to tabulate knots by representing knot diagrams using a pair of planar trees. This pair of trees have their edges labeled by integers, they have no valence 2 vertices, and they have the same number of valence 1 vertices. The number of valence 1 vertices of the trees is called the girth of the knot diagram. The classification problem of knots admitting girth 2 and 3 diagrams is studied. The planar tree pair representations of girth less than 4 for knot diagrams in Rolfsen's table are given.
引用
@article{arxiv.math/0508590,
title = {A New Way to Tabulate Knots},
author = {Lisa Hernandez and Xiao-Song Lin},
journal= {arXiv preprint arXiv:math/0508590},
year = {2007}
}
备注
17 pages, 6 figures